So I finally got a proper cable and the 32X is working, horay! Unfortunately, I am having problems with the Everdrive reading the SD card, so it may be a while before I get a chance to play most of the games. I did manage to play a couple space games and Doom, though. Sega made first-person space shooters for this like they did FMV games for the Sega CD.
EDIT: It turns out that it wasn't an Everdrive problem. The white ribbon cables inside the 32X needed to be re-seated. The Everdrive is much more finicky than regular cartridges which is why it was difficult to pinpoint.