76 Outside Mirror problem

You can see where the PO "fixed" it with a liberal application of gasket sealer on the ball. All it really did was make a mess. After reading this forum, I thought I would try the lacquer thinner approach to make the mirror fall out and see if I could tighten up the pivot. I had nothing to loose - worse that could happen would be I had to buy a new mirror. After a week in a lacquer thinner bath, the glass did not budge (but it did remove all of bubba's gasket sealer). I tried to help it with a razor knife around the edge to see if it would pop loose. All that did was chip the mirror.
Now that I had to replace the glass, I thought I would go with a more direct approach to get it out.
Turns out the glue holding the mirror on the four raised posts with a cross hatch was some sort of black silicone. The lacquer thinner hadn't touched it. Oh well, now I know. Closer inspection zeroed in on the problem. The left rivet has worked ever so slightly loose.

Any pressure on the retainer would add enough friction to the ball to hold the mirror in position. Now finally for the question for all you experts. I could either drill out the rivet and thread a hole for a replacement screw and washer, try to shim underneath the existing rivet, or tap the edge of the rivet with a punch to tighten it up. Any recommendations?

Floppy mirror problem solved! Now I just need to buy a replacement mirror. Still cheaper than a whole new mirror assembly.
Ground the rivet top off on the one side that was offset and off to the one side, couldn't be tightened anymore, tapped it (6-32) and used an e-clip as someone said in another thread somewhere
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