If you grind the head off, then take a punch to punch out the rivet, being careful to not punch on the frame, just the center of the hole, you might not have any damage to the 3/8" hole. Not sure how much of a swing on the hammer you are going to get under there though. That's where a 1/8 or so drill hole in the center of the rivet to relieve pressure could be the way to go.
While you are waiting for the parts, wouldn't hurt to spray some PB Blaster around the rivets.
