I myself consider Ki-44 as an adequate fighter for it's time. Problem was that IJA (IJN problems are for another thread, and boy does it have food for thought) air service have had Ki-27s in service through whole of 1942, and Ki-43 was with sigificant shortcomings itself. Main problem with Ki-44 was it's short production run - it was phased out in 1944, while Ki-43 was still being produced in August 1945 - and thus relatively small numbers available. So the new source of better fighters is not an addition to the Ki-44 force, it would've make possible to get rid of the Ki-27 ASAP, replace the non-produced Ki-45 as per this thread thus saving a lot of war material, as well as fuel when inservice, having a ready replacement for the Ki-43 etc.
Kawasaki making a good 1-engined fighter already by late 1941 is not a short-term solution. As never versions of engines are available it's performance and combat capabilities can be improving. Eg. swapping the earlier Kinsei type (1050 HP at 4 km; 'History of Mitsubishi engines' gives 1070 HP at 4.3km) for the later type (Ha 112 per Army nomenclature; 1100 HP at 6.2 km) is an improvement, as is the Ha-112-II as installed on the Ki-100 (1250 HP at 6 km). More power between SL and 5 km was achieved via usage of water-alcohol injection, as on the Ki-46-III. More engine power means that addition of firepower and protection does not hurt the performance.
Ki-60's handling was influenced by it's high wing-loading, in the time Japanese preferred low wing loading that gave better maneuverability. A radial of 560 kg (= Kinsei that makes 1050-1070 HP at 4-4.2 km) will shave some weight vs. the 680 kg Ha-40/DB-601 + 150-200 kg of the weight of the cooling system, ie. around 300 kg less.
One month late I finally got a chance to consult my book.
First i agree that Ki-44 was pretty good mid war, with the caveat that it could use heavier armament earlier. i'm not certain that the IJAAF can make do with it as their only front line fighter until the Ki-84 shows up.
Kawasaki making a good fighter earlier than historically may prove problematic. The Ki-60 seem not to have suffered only from manouverability issues on account of its high wing loading. For the first protoype: "The aircraft displayed some lateral instability, excessively heavy control and poor control response, it demanded an unacceptable long take off run in normal loaded condition; its spinning characteristics were considered 'dangerous'; its stalling speed was extremely high" Green, William and Swanborough,Gordon:
Japanese army fighters: part 1 Macdonald and Janes 1976: p20. Speed for the prototype was only 548 km/h, raised to 560 in the subsequent prototypes with 5000 meters being reached in six minutes. No significant improvement in handling was present, Ibid.
It's questionable if a radial would in itself have cured that problem, and unless it gave more power performance would suffer. Eventually the Ki-61 emerged as the 'fixed' Ki-60 so I see little chance of achieving anything wortwhile until the historicallyKi-100 becomes a possibility, granted that could probably have happened well before 45.
As for the Ki-46 it had the slow rate of climb and manouverability shortcomings commented on by others. Actually a study by the Army Aerotechnical Research Institute shelwed a projected fighter adaption in summer 1943 on account of these problems. furthermore its structure (apparently in the eventual service model), proved insufficiently sturdy for absorbing combat damage, ibid 51f.
I do not disagree that the Ki-45 was not a world beater even in 1942, but compared to what else options the Japanese Army actually had open to them, and certainly what they had in service, it was probably in some respects (fx fire power) the best they had in 1942 and for some time after that. I do believe the Ki-96 should have been purshued more vigorously.