If you do want to upgrade the Mac to a SuperDrive/FDHD model the easiest way to do so is to find a logic board from an SE SuperDrive/FDHD and swap it with yours. Since most compacts seem to die from analog failure there are probably a few folks on this board who could swap you one or you could look on eBay, even if it meant acquiring a dead SE and stripping it of its logic board (this will also get you some spare parts and possibly some RAM).
Alternately, if you're not using the SE's expansion slot, swap with an SE/30 logic board. It will fit fine in an SE case.