Your dremel with flex shaft and a burr or stone should work perfectly from inside the head tube. That's how I did it after the rivet spun when I tried to drill it out.

I used tiny stainless steel screws to reattach the badge. I thought the screw heads were too big, so I turned them down a bit. Screws make it easy to steal the headbadge, but I never let the bike out of my sight when It's not locked in the house. I spent months tracking down a Carlton headbadge and when I found one it wasn't cheap.