Cool, this is pretty much exactly what I was looking for.
Looks like I can pick up a 7808 for around 50 cents so I'll go ahead and pursue that route first. I've already set fire (literally) to a couple of wall warts with accidental shorts so I'll definitely be putting a fuse in the circuit as well
As for modifying the adapter itself - I'd really rather not mess with it, at least not at this phase. Just getting the casing open would pretty much ruin the adapter (it's a cheap one) and even then my fine-detail soldering skills are pretty horrid, so I'm not comfortable trying to screw around with replacing resistors in there.
If this project goes where I want it to I'll need the ability to draw significantly more than the 550mA or so needed for the LCD, so I'll likely end up acquiring/building a switching supply to handle that. In any event though that's quite a ways in the future.