After trawling the web for ideas (and some tries with a flat-head screwdriver that made a mess of the drywall), I landed upon:
- score around the edge of the wood with a craft knife (so as to make less of a mess of the paint, though I'm going to paint again anyway).
- use a flat-head screwdriver to pull the wood a little away from the wall, being careful to do this far from the nails where it's easier
- when the gap is wide enough, ease the claw of a hammer into the gap, and try to make the gap a little bigger.
- Put a "shim" (small piece of wood, or, in my case, a nice thin but solid coaster advertising McVities Digestives) under where the hammer would go into the wall, and use the hammer claw to push the wood away from the wall, nails and all.
The remaining closets are Amy's office (full of stuff, but otherwise just like Megan's), our closet (bigger, with a plastic hanging bar rather crudely screwed to the shelf), and the hall closet downstairs, which has a wood platform on the floor.
Oh, and I also rigged up something that would keep the mudroom door closed, involving the old door catch, a spare piece of wood, some nails (for the spare piece of wood) and a judicious arrangement of screws to fix the old door catch to the door jamb, and to hold it away from the jamb so I didn't have to try and chisel out a hole. (It's probably a temporary arrangement only, since I didn't hang the door properly in the first place, and, besides, the door is too small for the hole.)
I'm quite pleased with myself. Now I have to figure out something for dinner, including for Nathan, who doesn't eat much, especially if I cook it.