You've run into one of the gnarlier problems in Hobiedom. The gudgeon bolts thread into an aluminum plate laminated into the transom of the boat. The SS/aluminum interaction as well as the fragile mechanical properties of aluminum make repairs difficult. Also, unless you have ports installed in the back of the boat, you are only able to work from one side.

Repair suggestions in ascending severity:
1. Remove fiberglass from the transom enough to expose the now-headless bolts and remove them with pliers or some sort of threaded coupling. Reglass and rebolt.
2. Bolt extractors. Agree that this would be very tricky and the chances of going 4 for 4 pretty slim. Could end up with an even bigger mess.
3. Drill out/redrill for the next larger size bolt and retap the aluminum plate.
3A. Sounds like you have the 2 piece gudgeons. Get the newer one piece gudgeons. These require 2 new (tapped) holes anyway but I believe they use 2 existing holes so partial step 1/2 may be required.

Good luck!