Mineral spirits should be perfect for removing the leftover adhesive, but I would test it on another piece. Definitely no "hotter" that the mineral spirits.
I'm surprised, I don't know why, but I thought that lexan wouldn't blast very well at all, given that its plastic. Definitely a lot of options as far as acrylic and lexan trophies/awards, etc out there.
When you say "edges got roughed up" you mean the edges of the piece of lexan? What I usually do with lexan or plexi is just a fine file, or you can drag a sharp razor blade/utility knife down it to bevel the edge past the chips. To keep it from happening, I have put either masking tape or pieces of paper apptape on the edges.
The rubnbuff turned out really well on there!