I did look to see if the resolution had somehow been changed. However, all the affected emulators were still set to their defaults. I believe my problem is that I always update the OS/Firmware alongside the RetroPie update and the most recent changes are reacting poorly.
Since I really don't want to downgrade anything, I'm just going to wait for the issues to be fixed upstream. In the meantime, the only emulator I can't trick into it's proper aspect ratio is Daphne and I can just adjust my television to squeeze the image to 4x3 when I want to use it.