That depends on their strategic situations. If Germany (and Japan) are desperately holding on for an extra few months (for example, due to a much less disastrous Bagration), you may see the Horten 229 V3, Me P.1101, and Ta 183 prototypes all fly, and maybe the HeS 011 of you're lucky.
The HeS 011 was probably a dead end (it might have worked, but not at the power/efficiency targeted and would be very costly/work intensive tomanufacture due to the precision machined mixed-flow compressor stage). The Jumo 004D and E (including afterburning variants) and BMW 003D (using reaction rather than impulse compressor blading) would be the more realistic engines approaching the 'class II' thrust range.
That and further Me 262 derivatives would also probably be the best bet, had the Germans been in any position to continue production. (engine upgrades would be most likely, be it 004 or 003 derivatives, and possibly adopting the leading edge wing root extension tested on the HG-I)
The 003s going to the He 162 probably would have been more worthwhile mated to Me 262 airframes as well.
The N1K was intended to be a land-based fighter for the IJN and by that point in the war, at least the IJN was being realistic, because their carrier force was nearly all submerged...
Neither was the J2M I suggest canselling. And the engine was ready for the N1K1-J which was build in some numbers before the redesign into N1K2-J
I suppose the better question would be: would an alternate N1K-2 like design (but with the earlier Kasei engine) also be adaptable as a carrier based fighter? (wing loading/stall speed, wheel pressure, and performance with tail-hook equipped and CoG shifts addressed would all come into play)
In the context of that thinking, wrong and misplaced as it was, the J2M made perfect sense. It was everything the Zeke was not......powerful, well armed, protected, fast, big engine. That it suffered massive delays and technical glitches was not really the fault of the aircraft, more a function of Japanese over confidence as to their capabilities.
Abandoning the extension shaft arrangement and going for a more conventional short cowling (possibly still using a cooling fan or perhaps resorting to a cuffed propeller to help facilitate a tighter cowling and larger/streamlined spinner) should have saved a great deal of time and difficulty in production and service regardless of sticking with the interceptor requirement. (Curtis and Focke Wulf both attempted extension shaft and odd cooling arrangements for radial engines and abandoned those in favor of more conventional arrangements, with or without fans)
The Japanese had a partial solution to the A6M problem staring them in the face. Stick the Kinsei engine in the Zero airframe in 1942. It had about 15-16% greater displacement ans should offer a similar or slightly less increase in power for only a slight increase in diameter and weight. It was done at the end of the war with the A6M8.
The Kinsei combined with structural reinforcement (including thicker skin) would be a significant adaptation. (along with armor and self-sealing tanks) You'd lose some range, of course, and CoG shift might be an issue, but it's not all that different an engine change than the F2A saw going from the F2A-1/B.239 to the F2A-2 or Buffalo Mk.I, or what the A6M already dealt with switching to the heavier Sakae models. (making engine and armor changes at the same time would also allow some degree of controlling CoG by using armor plate weight and location as ballast)
There's also the Ha41, but that's a bit larger and heavier still.
The Japanese had enough trouble developing the engines they had without trying to fool around with total redesigns of antiques like the Ha-9. The Russians didn't just tweak the Hispano to get the M-105, it took them years and several intermediate steps (engine models) just to get to the 1100hp M-105P version, they also added almost 200lbs of "improvements". Having the Japanese devote 10s of thousands of man hours to developing these engines could only be a benefit to the Allies.
But would it be more troublesome than getting the licensed DB-601 into production? This could include avoiding the more extensive changes the Soviets made and remaining closer to the performance range the French managed with development of the 12Y (not 12Z) but possibly making further supercharger improvements or at least implementing 2-speed drive.
Other than that, the Jumo 211 might have been easier to mass produce than the 601 (and the 211F would seem to line up with Ha-40/Ki-61 production) of course they wouldn't have been able to accommodate the Ho-3 in that case, but the Ho-5 would be more attractive once it arrived anyway. (aside from any imported MG 151s ... and precluding any sort of unlikely cooperation between Army and Navy weapons production to allow the Oerlikon based guns to be used)
The Hispano engines seem better for a potential early/pre-war development as a direct follow-on for the earlier Ki-28 fighter design.
Aside, of course, from just shifting to radial engines entirely and focusing more on something closer to the Ki-100 from the start. (or prior to that, an earlier development around the Sakae stemming from the Ki-28 might make for something significantly better than the Ki 43) No possibility of unsynchronized centerline cannons in that case, though.
The Ki 61 was bigger, with huge internal fuel load (199 US gals), and, as war progressed, improving armament. The 'Ki 61 lite' should be interesting - swap the wing between historical Ki 44 and Ki 61? Or, install the Ha-109 on the Ki 61 to produce the 'Ki 100'
The Ha41 followed by Ha109 seems reasonable for an aircraft of that class, assuming they didn't go for the Jumo engines. (or in addition to those in either case -any 12Y derivatives would probably top out too low to work well on something of the Ki-61's size, but again better for something closer to the earlier Ki 28 )
the Zero needs the Kasei dearly.
The Raiden with 'plain vanilla' Kinsei (= no ext. shaft) should also be KISS business. The wing is already tad bigger than of Fw 190.
I think you've got Kasei and Kinsei switched there. (Kasei would be a slightly larger/more powerful engine than the Sakae, the Kasai is in another class entirely and more akin to the BMW 801 or R-2600)