OK, I lied.
Apparently I don't know my large African animals. The brand I bought was Rhino, not Gorilla. Sorry about that.
That stuff was a bust. It wasn't an actual tape but a sort of glue film. Long story short, it was just way to hard to try to work with. Went to another store, got Scotch brand which is at least made by 3M.
That worked a LOT better.
I had some very tiny pieces that it didn't hold very well but they were only about 1/2" long by 1/8" wide. I don't think they had enough surface area to stick to anything when attacked with a Dremel tool. Even so, just bracing them on the scrap with a little stickiness was better than nothing. I didn't clobber my nails/flesh.
Larger pieces (dime to penny size) stuck pretty solidly though and I was able to get them up without undue problem. I didn't have a lot of time to play with it as I had Father's Day at dinner tonight. Tomorrow I will try long, thin pieces with sort of odd shapes. It looks very promising from what I've seen so far.