I really enjoyed reading this thread and there were several good posts in it. Another good one. The idea of the Japanese opening a second front against the Russians as a way for the Axis to win and for Japan herself to acquire some badly needed oil is very interesting indeed, especially as an alternative to attacking Pearl Harbor. It would have put the Americans and FDR in an extremely awkward position.
But let me play devils advocate a bit.
I'm not sure the Soviets would have been overwhelmed by the Japanese the second time around. Compared to Khalkhin Gol in 1939, by 1942 the Soviets arguably had advantages in their land army. By 1943 I think it is not debatable that they had a substantially superior land army.
In 1942 (this is from memory so forgive me if I make a couple of errors)
Soviet Fighters
I-153 - 4 x 7.62mm, 276 mph
I-16 / 24 2 x 20mm, 2 x 7.62mm ~ 320 mph
LaGG-3 1 x 20mm, 2 x 7.62mm 330-340 mph
Yak-1 1 x 20mm, 1 x 7.62mm ~ 350 mph
Yak-1B 1 x 20mm, 1 x 12.7mm ~ 365 mph
Yak-7 1 x 20mm, 1 x 12.7mm ~ 350 mph
Yak-7B 1 x 20mm, 1 x 12.7mm ~ 360 mph
Lavochkin La-5 20 x 20mm, ~ 370 mph (guessing)
MiG-3 1 x 20mm, 2 x 7.62mm ~ 400 mph at high altitude, 314 mph at sea level (per Wikipedia anyway, probably a bit less in real life)
Hurricane Mk II 4 x 20mm or 12 x .303 ~ 330 mph
Tomahawk 2 x 12.7mm (some had 4 x .30 cal) ~ 350 mph
P-40D/E 4 or 6 x 12.7mm ~340 mph
P-40K 6 x 12.7mm ~ 360 mph
Soviet Bombers
Su-2 dive bomber - 6 x 7.62mm, 300 mph, dive bomber 1,300 lbs bombs, 680 mile range
Pe-2 dive bomber - 1 x 12.7mm, 3 x defensive machine guns, ~330 mph, 2,200 lbs bombs, 720 mile range
Il-4 bomber 3 x defensive machine guns, ~ 250 mph, 2,100 lbs of bombs, 2,400 mile range
SB bomber 4 x defensive guns, ~1,000 lbs of bombers, 1,400 mile range, 280 mph
A-20
B-25
Il-2
Bristol Blenheim
Japanese Fighters
Ki-27 2 x 7.7mm, ~ 270 mph
Ki-43-I 1 x 12.7mm & 1 x 7.7mm, ~ 300 mph
Ki-44 ( very small numbers available) 4 x 12.7mm mg, 370 mph
Ki-45 heavy fighter ~ 330 mph, 1 x 20mm cannon, 1 x 37mm cannon, 1 x defensive LMG, 1,200 mile range
Japanese Bombers
Ki-21 - 300 mph, 1,700 mile range
Ki-48 - 314 mph, 1500 mile range
Ki-49 - 306 mph 1x 20mm cannon, 5 x 7.7mm, 2205 lb bombs, 1,200 mile range - armor and self sealing fuel tanks (later models).
Ki-46 - 360 mph (recon)
Advantages for the Russians - generally speed, they have a lot of relatively fast and agile fighters and two pretty fast bombers, cannon armament, armor and self sealing tanks.
Advantages for the Japanese - maneuverability, range, build quality, altitude performance.
The Japanese would have some trouble with the Soviet bombers and the more heavily armed Lend Lease American bombers (as they did in the Pacific and in China) due mainly to speed but also to lack of heavy firepower. The Pe-2 would excel and the Su 2 may have been pretty useful too. The Il-4 would be fairly vulnerable and the A-20 would be about average probably. The Soviets did have their heavy fighter the Ki-45 which had the range and altitude capacity to be a pretty good bomber interceptor.
The Soviets had P-40s which we know did quite well against Japanese army aircraft.
On the ground,
The Soviets have KV heavy tanks, T-34 /76 mediums, and T-60 (20mm gun) and T-70 (45 mm gun) light tank, and American M3 Stuarts and M3 medium tanks, and British Valentines. They had American trucks and halftracks and plenty of 45mm and 76mm AT guns. They had Katyusha rockets and PPSh 41 sub machine guns, lots of artillery and various medium and heavy machine guns. Now it's likely the best of this kit is going to be thrown into the breach against the Germans, including probably all of the KVs and most of the T-34s.
But against the IJA they should have enough T-34s AT guns and artillery to spare to have major advantage in armor, which would be particularly telling on the open steppe or the fringes of the Gobi desert. T-60 and T-70 light tanks were not particularly useful against the Germans, but I think they could have been pretty good against Japanese tanks and tankettes - and they had more than 12,000 of these light tanks! Keep about 2,000 in the West for scouting or screening flanks etc., and send the rest to fight the Japanese. Do the same with the M3 Stuarts and M3 mediums, and maybe some of the Valentines. They would all be much more effective against the IJA than against the Germans.
The Japanese have their highly motivated and disciplined infantry which does mean something, and probably equals out the Soviet advantage in armor and things like submachine guns somewhat. But overall in the land war I think you have a stalemate. The Soviets might lose more like they did at Khalkhin Gol but assuming that, as in that battle with general Zhukov in charge, they have competent leadership, they should be able to manage a fighting retreat with a lot of counter attacks and make the invasion very costly for the Japanese while actually getting some use for a lot of equipment that was virtually useless against the Germans.
Reverse Siberian transfer
The main theory I have is along those same lines with the planes. They (the Soviets) had a lot of planes that were almost useless against the Germans (essentially because they were too slow) but might prove of some merit against the Japanese who themselves had slower fighters. The I-16 which was their best fighter at Khalkhin Gol is now up-gunned with a pair of excellent 20mm ShVak cannons. That makes it a potentially dangerous opponent for Ki-27s and even Ki-43s and any Japanese bomber they can catch. The I-153 is improved a bit and carries rockets, falling into more of a ground attack niche but with it's excellent maneuverability it should be able to tangle with Ki-27s and Ki43s somwhat. LaGG-3s aren't very good in 1942 vintage but would probably do better against Ki-27s than against Bf 109s and could catch Ki-21 bombers. MiG-3 would be a pretty good interceptor against any high flying Japanese bombers or the Ki-45 heavy fighters, though I suspect they would be dead meat against a Ki-43 if caught (they should stay up high).
The interesting bit of course is how do the Yak fighters stack up against the Ki-43-I. I'd say the Ki-43 probably dominates the I-153, I-16/24, LaGG-3 and early Yaks - though probably not enough to avoid taking steady losses. The later model Yak 1b and 7b and the La 5 I'm not so sure. They are comparatively fast enough to hit and run and have good enough climb performance and acceleration to fight in the vertical. So maybe about even, who knows. The later model Yak-1b and the La 5 might be able to run rings around the Ki-43 down low anyway. The Ki-44 could give them a run for their money but only about ~100 are available in 1942.
The Soviet bombers also pose a problem for the Japanese, in that they are relatively fast, have armor and self-sealing tanks, and the Pe-2 in particular is not only faster than the Ki-43 but it also has fairly heavy defensive guns The Su-2 and the Pe-2 are both dive bombers and the Il-2 is a close support / point attack bomber of course. Meaning they are arguably more accurate for ground support than any of the Japanese Army bombers which are all level bombers. I think the Ki-43 is going to have a hard time intercepting Pe-2s and may struggle a bit catching Su-2s. Il-4 and SB are probably within their grasp. The Il-2 is going to be a challenge to bring down with that light armament in the IJA fighters. The Japanese also don't have anywhere near the kind of AAA capacity the German army has, especially in terms of mobile assets. I suspect if even a small number of Il-2s could prove to be a major problem for the Japanese army.
That said the Japanese bombers pose some problems for the Soviets with their long range, relatively high ceilings and high speed. The Ki-49 in particular is going to be probably fairly immune to interception except maybe from the MiG-3s.
The other key issue is how many of the better fighters do the Soviets send East. They are probably going to keep most of those Yak-1bs, Yak-7bs, La 5 and Kittyhawks on the front line. And of course their Spitfires which I didn't even mention because they won't go East. Instead they will probably send all or most of their remaining I-16, MiG-3, Su-2, Hurricanes, LaGG-3s, Tomahawks and a large proportion of their I-153, early Yak 1 and Yak 7s, as well as most of their remaining Tupolev SB bombers and Blenheims. If they were smart they would send a few Il2s and some Pe-2s, and maybe the majority of their B-25s since they didn't find these could handle German AAA in daylight. We know B-25s did well against the Japanese in the Pacific. Chennaults 23 FG had just a few of those and wrought a lot of destruction with them. The Soviet Navy had an important niche for the A-20s so they will probably keep those in the Baltic.
How it pans out
So I see it like this. Against basically the rejects from the Western front, the Japanese will face this motley assortment of kit in Siberia, initially I see the Japanese having a slight advantage. Their ground army has excellent discipline and a high morale, their pilots are good and their aircraft are superior in many respects. But even if we say the Japanese are initially winning at a rate of roughly 2-1 or 3-2, as they did at Khalkhin Gol, the attrition rate will start to catch up with them especially in the air battle. In 1939 I don't think the Soviet fighters had armor or self sealing tanks, but in 1942 I believe most of them did. The Soviets were also good at recovering & repairing their tanks, and they adapted quickly to tank warfare. If they had even a few T-34s and maybe some heavier M3 mediums and Valentines and the like, they should be able to quickly assert a decisive advantage in armor. Probably artillery too. And if they bring even a few Il2s and Pe2s this should become more perilous for the IJA. I could see some Japanese forces initially victorious but suddenly collapsing once the Soviets get a relatively thick concentration of armor together for a well coordinated attack.
The Japanese never had that many Ki-43s to begin with by that time and they would begin losing them too quickly in this scenario I think. The initial advantage would shrink as the Soviet fighters improve (especially in build quality) through the course of the year of 1942 and the Soviet pilots learn the lessons of war. Newer Soviet planes are going to keep coming out. More of the improved Yaks. The Ki-43-II will arrive in December of 42 but it's not a major improvement, incremental at best. The Soviets on the other hand will soon have the La-5FN and the Yak-9 which I think should have a substantial advantage over any model Ki-43 at least at lower altitudes. I could imagine the Soviets bringing a squadron or two of their biplanes to join with the faster newer fighters, so that the Ki-43 pilots will be in trouble if they turn and in trouble if they boom and zsoom. The Japanese will get more of their fast Ki-44 and then some Ki-61s in 1943, but probably not enough to make a difference. And if there are Il-2s on the battlefield then the fighting is going to be focused down low over the army like in the West.
My one big question is based on the Soviet Eastern oilfields. Where were / are they? How far would the Japanese have to go? If the distance wasn't too great, like something they could reach in say 2-3 months of steady gains, maybe the IJA could take it in a costly Blitzkrieg action. Then they have to hold it so the battle keeps going. How much of a hit losing that oil would be to the Soviets is another interesting question.
But it seems to me like the Soviets had literally thousands of tanks and airplanes that were all but useless against the Germans but could do some damage to the Japanese. The Soviets made 6,800 I-16s between 1934 and 1942. Probably at least half of those were gone by the time this hypothetical war starts up but that still leaves probably at least a couple thousand to send. They built 6,500 LaGG-3s, mostly before 1943. Send 2,000 of those to fight the Japanese. And you have 3,000 Hurricanes that have been sent to Russia. They can't help much against Bf 109s any more. Send however many are left, 500 or 1,000 to the East. Now just with those three types you already probably outnumber them substantially in fighters. They have made roughly 6,000 T-60 tanks and 6,000 T-70 tanks. Again probably a good number are already gone or unserviceable by early 1942 but no doubt quite a few are still left. Put them on the train and send them to fight the Japanese. They built an astounding 35,000 T-34s with the short 76 mm gun. Surely they could spare 2-300 or so to fight the Japanese. A few dozen Katyusha rocket launchers would also be nice. And etc.
While the risk of collapse in a war on two fronts was real, a successful counterattack, maybe after a nice feigned retreat and a double envelopment, could have been a major morale boost for the Soviets and a major shock for the Japanese. The Soviets could even move out to take a bunch of land in Manchuria and gain some resources.