Norbert,
I wouldn't recommend you to drill the rivets from the mast plate because, in my opinion, you will never obtain the same result of the manufacturer in replace them. Consider two things: 1. each one of the rivets must be inserted in a small goblet to ensure the water resistance of the mast, which I presume you want to keep; 2. you are working on carbon fibre...
This last considaration is driving me to a different solution: To insert a stainless steel thick tube (of the same external diameter of the original hole in the plate) into the elongated hole to distribute the strengh on a larger surface, being prepared to replace the tube every... year, couple of years, never more!
This solution should be better than welding anything or drilling factory rivets.
I'll keep you informed on results.