Goof Off went well, I'm pretty sure I got all the glue off.
Finished shaping the headstock with sandpaper. Took ages but the result was worth it. Still needs to be sanded smooth, but the shape's where I want it.
Took the body up to 240 on the back and sides, haven't touched the front yet. The marks I was worried about look like they're completely gone. My forearms and fingers hurt.
Based on Wazkelly's advice
I guess the next step is to (lightly) sand the veneer at 320 and then stain. Might wait until it stops raining though. After each coat I plan to hang the body in the cupboard that contains the central heater. It's not the warmest place in the house, but it's always got a small draft through it from the intake and stays around ~22-24 degrees celsius when the heater's on.