Well, I finally got to look at the thing again this weekend (the shop I'm using is 100 mi away), and it wasn't quite as bad as I thought. I hand sanded it down almost to the wood with 220 and 320, and it looks ok (ie, I didn't destroy the veneer on the plywood). I haven't stained it yet. There's still small scratches on the top from the orbital sander (!!!), but I can't seem to get them out, so I'm going to hope that they hide themselves under the stain and poly.

I am the Doctor, and THIS... is my SPOON!