Parsifal,
So far we've only been listing the manpower equipment available to the Japanese, so we're not really speculating much in regards to strength. Simple addons to existing equipment can't really be said to be highly speculative under these circumstances either, as based on where the fighting was expected to take place the various equipment available would be adapted towards it as best as possible.
If we were to really start speculating a lot then we might as-well have concluded from the start that if the Japanese planned a land based invasion of the USSR instead of a war in the Pacific, then tank production would've recieved a much higher priority status and thus a lot more tanks would've been produced in the 1939 to 41 time frame. This would also be the most likely thing to occur actually. But for now we're just gonna stick with what was available in 1941 at the time where a war in the Pacific had been the original goal.
Furthermore in the case of an invasion of the USSR, China wouldn't have been given much priority at all. The Japanese weren't importing any meaningful amount of important resources from the place yet anyhow. So it would've really been no concern to the Japanese at that point, esp. as they would know that after the defeat of the USSR an invasion of China would prove a lot easier. All they needed to do was hold on to the areas already conquered, and they had over 2 million reserves ready for that task. Way more than was ever needed. The airforce over there wasn't needed either. It was just about having the reserves dig in and hold the ground already gained.
Moving on..
The Japanese air strength:
By July 1941 around 600 A6M2 Zeros had been produced, of which 400 had so far been delivered to the Navy, 108 of which were used for the raid on Pearl Harbour. Another 200 were stationed in mainland Japan, just sitting there waiting for Navy pilots to come fly them (Sounds cute eh ?

).
But like you already stated the IJN had only a little under 300 pilots for its Zeros, with an extra 100 a/c standing without pilots.
However in the scenario suggested the IJN would be stationing all its Zeros near the Russian east coast, while the entire reserve would be handed over to the IJA, which was a total of roughly 300 a/c, 100 of which were from the IJN reserve.
So combined the IJN IJA could muster around 600 A6M2's for the invasion of the USSR. Half being flown by the Navy Airforce and the other half by the Army Airforce. The Japanese knew that they had one of the worlds best fighters in the A6M2 and would've no doubt wanted them all ready in an invasion of the USSR.
In addition to this around 300 or so newly built Ki-43Ia's were standing ready in Japan. These would've been handed over to the army.
So the Japanese could at least gather roughly 900 new fighters for the invasion of Russia, which would be opposing the roughly 1,400 mixed bag fighters of the VVS. And knowing that the Japanese fighters pilots were in general much superior to the Soviets', this would've proven no hard task for the Japanese. The VVS would've been swepped from the skies in a relatively short space of time. Also while the VVS pilots stationed in the east were destined to later become Guards, at this point in time (1941) they didn't have much experience, and it must also be said that throughout the war the Germans in general didn't notice any real distinction between guards regular pilots, it was all the same to them; There were the occasional good ones, as Hartmann said.
Also lets us not forget the number of Ki-27's, A5M's A4N's available either ofcourse.
On top of this the Japanese also had a good number bombers ground attack a/c ready for operations. These included the Ki-51, D3A, B5M G4M1 etc etc. These would be tasked mainly with destroying Soviet airfields tanks, and once far enough in land also target Soviet production facilities.
The numbers available included:
G4M: >100 (~120)
G3M: >400 (?)
D3A: >250 (~300)
B5M: >150 (~200)
B5N: ~250
Ki-30: 704
Ki-49: >100 (~120)
Ki-51: ?
Ki-46: ~60 to 70
So plenty of a/c were available for role of ground attacks bombing.
Next are the land based forces available to the Japanese;
By mid 41 the Japanese had at their disposal 2.25 million trained soldiers and another 4.5 million armed reserves. All of the trained soldiers would be needed for the war against the USSR, with at least an extra 1.5 million reserves standing ready. ~2 million could be stationed in China over time.
To add to this the trained Japanese soldier was just as well equipped as the average Soviet soldier, and better trained in many respects as-well.
As for armour, the Japanese had amongst others available:
Type 97 Tankette: 557
Type 95 Light tank: ~500
Type 97 Medium tank: ~850
So a total of around 2,000 tanks, not a really impressive number, but these tanks had proven very effective in forested areas, and they were certainly a match for the far majority of the tanks that the Soviets could ever afford to deploy in the east.
So that means that for the invasion of the USSR the Japanese could have available atleast 900 new fighters (+ the older a/c), over 1,000 bombers ground attack a/c, ~2,000 tanks, 2.25 million trained troops 1.5 million armed reserves.
This would be more than enough to take a lot of pressure off the German army in the West while at the same time putting an unsustainable amount pressure on the Soviets.
Next comes the navies, which I'll deal with later, the Japanese had it all over the Soviets there.
But the whole point of the Japanese invasion would simply be to divert as much of the Soviet manpower as possible, letting the Germans do the true damage.