Well, it's progress.
Step 1, drill out the existing rivets using a #30 bit. No problem.
Once you have it in your hand it feels much smaller than I imagined.
Step 2, here's where the options fall. I realized that without some sort of 'gripper' there was no way to keep the new screw from just spinning. My solution was to take a washer, Dremel off the sides so it was sort of square and forced it in the cavity using the screw and nut. Then I applied a liberal amount of RED locktite.
Step 3, re-attach using 1/8" x 1/4" closed end pop rivets, covered with a gray RTV. (photo)
Step 4, clean up.
The fasteners are 10-24 x 3/4" stainless truss head screws. Truss head screws have a larger flatter head profile. On the outside is a washer, then a regular #10 nut, the window bracket and a #10 nylock nut.
Sorry for the lousy picture, hopefully, it shows the concept.
It was common sense enough I'm going to replace the other three Dzus contraptions, but I'm going to try a star washer as my 'anchor' inside the cavity.
Thanks for the wealth of good advice from the pioneers, I took it all, used what seemed right for me. The system, mostly, is that proposed by Air Miles.