I have actually done that same repair. Depending on the age of the rivets, they eventually loosen up. I was able to just drill them out and replace them. It worked for me. You have nothing to loose in trying that first. The problem you may encounter is if the holes have actually widened because of the movement. In that case you will need to either use a larger rivet and/or drill new holes.

Make sure you seal the rivets and the mast base with silicone. Not as important as holes near the top of the mast, but if you turtle, it will keep water out. It is actually a good idea to have a small drain at the bottom of the mast, just in case your mast isn't completely sealed, to let water out. The mast is upright most of the time, if you're lucky anyway. :-)

Hope you are successful. Let us know.

Sail Safe. HD.