You'll get much better results with a larger diameter, downcut bit. I'd rough cut everything with a 1/8" downcut, leaving about .01-.02.
Then finish cut with a 1/16" downcut. Climb cut might give a lightly better finish.
I think the only way you'll be able to keep the small details from breaking off is to glue the sheet down to a substrate, and use a solvent to remove the sheet after cutting. When I've done something similar, I'd glue them down with contact cement and use laquer thinner to remove them.