Is there a way to force the player to defeat a minor enemy (or a group of them, preferably) to progress? I already built a room for this in one of my levels before realizing that there is no way to put keys in enemies, which foiled my original plan.

There is a very roundabout way by using spawners using their limit property. You'll need to put one somewhere offscreen, ensure it's loaded and have it detected within your arena for its limit. once the enemy is killed, the spawner will be below its limit and spawn a new enemy, which you can use to trigger a contraption. (eg. goomba steps on noteblock, dispenses shell, hits switch, key drops from sky).

Here's an example: