Thoughts on drilling holes thru good paint?

I would definitely not use a punch, that would in my opinion, increase the risk of the chipping, particularly is there was an adherence issue in that area.

Mask the area with quality masking tape, and use as many 'steps' as possible, starting with the smallest drill bit possible.

Also, if you have some touchup paint, I would use it in the new holes. Not just for rust, but to insure that the paint around the hole doesn't lift.

If you are really worried about the paint, another option is to cutoff the studs, fill the emblem with bondo, and use 3m 2 sided tape (3m 03609).