Help with staining disaster.

Gallery here

Making a thing for a teacher friend and trying to figure out what went wrong. Bare wood looked pretty ok. It is oak veneer plywood and I didn't think I would have much issue using a gel stain. I gave it a coat of gel stain which looked passable. I then coated it with thinned poly and the last two pictures happened.

I did a test piece first, then tested on the inside, and it all looked good until I got to the top. The top is the only part where they stain is coming off in blotches. Could this be because I paid more attention to it with sandpaper? Any advice on where to go from here? I can sand and paint if need be but mostly just want to understand why it happened.