I just spent most of two days driving rivets out of smoke jumper polaski's for a customer. I found early on that the internal pressure would cause the rivet walls to collapse on the drill bit and stop it from turning, or, if really tightened in the superchuck, break and spit painful shrapnel at high velocities.
I finally found the best procedure, drill almost all the way through with a drill about 1/2 the diameter of the rivet, in stages to evacuate all the chips, and using MolyDee. Then over to a solid vise and with a punch slightly smaller than the hole drive them out. The heads were drilled off first with a larger drill.
The rivet areas were drenched in Kroil two days earlier to boot. It was a dirty nasty job, I took it on because I didn't want to ask anyone else to do it.
That's an extreme example, but drill almost all the way through with a drill sized a few thousandths over 1/8", Kroil too of course, and drive it out as someone holds a mass against the opposite side, or set it on a steel bench top.
But I'd try a hammer and punch first with Kroil, again, to be effective it has to have mass behind it or you will just jar the poor thing.