Well, a very helpful dude over at Sega-16 created some Game Genie cheats for this game that make you jump higher, thus making the game a lot more playable. The jumping animation gets a little screwed up, but at least the game can actually be enjoyed all the way through now. Here are the codes:
WCYA-CACW
Jump much higher while standing still
WCZA-CAE0
Jump much higher while running.
Note that the first code will glitch the first level, you'll just fall through the floor at a certain point. So just use the second code. There's really no need to have both of them enabled anyway.