I actually don't fly the KI that much. I really only use it when I think I will need ords for something and there won't be much or any ack and I will have to dogfight later with it. I will say this though, I have never had a problem with it wanting to snap roll on me. Just last night I fought against 2 109's and one I took the fuel on and after watching the film saw that he ditched (that is why I did not get kill message) and the other hit the ground hard after I got a single ping on him. I had flaps full out just trying to keep up with these guys, not to mention working throttle and the hat switch to the point of my fingers hurting. The KI does go from flap speed to a climb very well and can surprise the enemy many times, that is the way I got the one that ditched, he tried to rope me and I got within 400 and took the shot as he and I both were stalling. I would say the key to defeating the KI84 with most planes is going to be your ability to judge energy differences so you know when you can use a roping or BnZ techniques.
BTW luck was on my side against the 109's because these guys should have blown my tail off. Both of them are very good virtual pilots and I am sure that in a 1vs1 rematch both of them would beat me in the first 1-2 turns, but sometimes luck is your only ace in the hole.