Not too sure if the rivets are the same but I've drilled out plenty of rivets in my cousin's different race cars, and found some item's riveted on my truck that needed replacement. They weren't bad at all until I got to the rivets that held in the window motors. Those were a pita to drill out as they have a small pin in the center of the head. Most of the rivets I've dealt with, I've been able to use a manual rivet gun to install. It sounds like your rivets are much more heavy duty.
Anyway, I haven't done much riveting with fiberglass and definitely not on a Corvette. The best person here for technical advice is Manny (Manny@Dasilva). Send him a message and he should be able to get back to you.