The problem was that both games re-enabled interrupts right near the start of their interrupt routines and the timer interrupt was occurring too often.
Sadly Kirby's Dream Land 2 doesn't even start [sad]. There are also plenty of bugs in the games, even if they work. I figure there's a bad opcode someplace, but I've gone over them like a billion times and it's really getting tedious.
I've also been trying to combat the sprite flickering technique a lot of games use(the Mega Man series being the worst offender) by blurring the last frame with the current one. Here's what the first attempt yielded.
I actually tried playing through the level like this, I don't recommend it.