I ran into an issue drilling out the head of a plastic dino last night (don't ask) that the material stretched to accommodate the drill bit but then shrunk to make inserting a rod quite the challenge.
Anyway, I'd probably suggest pre-drilling the post holes and then chop and fix the figure. I am a bit surprised that the paint jobs were impacted as I find drilling with my pin vice rarely does anything other than drill a hole. That could be an issue with the paint bond to the material of the figures? I have also found that PCB (printed circuit board) bits come in a nice array of mm sized bits and are far superior to using a wood bit that I would use in my drill. You can get get a nice set for around $11 USD
I have bits from .3mm - 2.0mm in .1 millimeter increments. That was a big game-changer for me.