The KI-44 was less maneuverable than the KI-43.
It's only strong point was it's heavier armament and even then, the KI-44 and KI-44-II weren't available in any great numbers until 1943/44
And the P-40 was used to being bounced from above, that was the IJN's favorite tactic - from above and out of the sun. The AVG was well aware of this and their countermeasures were to turn into them and face them head-on. Old-school tactics.
Yes and this is what the British eventually figured out in North Africa, though it took them almost a year. Their original Tactic against Bf 109s was the defensive fighter circle - which worked except when you had guys like Joachim Mariseilles who knew how to attack it, and it was obviously very limited.
In Mid 1942 the Australians apparently initiated a new Tactic of turning the whole squadron into each attack and opening fire with all guns at convergence. They would wait until the last minute and the squadron leader would call on the radio "Prepare to break." and then "Break. Break. Port now." This apparently had a very discouraging effect on attacking Bf 109s and MC 202. Seventy two .50 cal machine guns aimed at you at full auto even for a second or two was somewhat intimidating. If the attacking fighters weren't very disciplined about breaking off their attack and
climbing away at high speed, they could then be pursued further.
It seemed to coincide with some kind of mysterious improvement in performance of the P-40s allowing for the higher power. Either due to newer Kittyhawk models or overboosting or both. Australian pilots coming from the Middle East apparently brought this strategy with them to the Pacific.
This quickly spread to all RAF Kittyhawk units. They also began pursuing attacking Bf 109s that did manage to make an attacking pass, which they usually followed by a high speed climbing turn to the right. Later model P-40s apparently had the 'juice' to follow them up into that turn and get a burst or two off. They continued this until the enemy planes either gave up or disengaged, or - if they had to press the issue to get at medium bombers or protect their own airfield for example, continued to engage in which case they would end up in an equivalent E state and the P-40s would start to get the upper hand as the dogfight inevitably descended downward and devolved into individual chases of 2 and 3 aircraft.
The strategy, adopted in the CBI, the Pacific, and North Africa, and also by the Soviets, is apparently a major part of what enabled P-40s to continue being used even where they faced attack from above all the way through 1943 and into 1944. I think it's a major part of he puzzle.
The US fighter groups also began launching attacks against the German air bases. This helped a lot - there was usually a small CAP of 2 or 4 fighters, but most of the enemy planes had to scramble and climb up from below, putting them at a major disadvantage, as medium bombers dropped bombs on their base.