I figured out a workaround for the problem: When you switch levels while playing (no matter if normal play or simulation), the possess/eject option gets carried over. My menu doesn’t yet depend on a player character being present from the start, so loading that, possessing, and making my way to the level in question does the trick. Quite tedious once the cumulative size of the levels grows beyond a certain point, but better than nothing.
For those who don’t have the patience to go through all your levels: You can create an additional (potentially debug-only) level select map, from where you can load all your levels. Make sure it doesn’t depend on your character being possessed right away. Then load that, possess, and load the level you want to debug from there.