I've gotten 3 more floppy drives to use, bringing the total to 5. Unfortunately, 2 floppy drives and 2 HDD drums was already causing power issues over USB, and now the system pretty much won't power on. I guess I shouldn't be too suprised.
I attempted a quick hack by connecting a spare 12V power supply to a 5V linear regulator, but it wasn't long until that overheated. I guess I'm going to have to use a proper power supply now.