Looks like I've got my work cut out for me this coming weekend. I'll pick up some Blaster and my left handed bits and give drilling out the bolts a go. Hopefully using care and some appropriate guide blocks will do the trick, and I'll be able to clean up the threads in the backup plate with a tap and be done. If not, I came across a "broken screw extractor" today which could be used as a last resort. It's essentially a 3/8" diameter hardened steel tube with saw teeth milled into both ends, and it has a bore of slightly more than 1/4". I tested it, and it does cut aluminum, although because it has no set to the teeth, it has little clearance for the chips and has to be extracted every 5 seconds or so and cleared. Using a guide block with a 3/8" hole, I could cut down around the outside of the bolts, through the glass and the aluminum backing plate, and remove the bolt like a wooden plug in a hole saw. McMaster Carr catalogue has a stainless threaded insert for a 1/4-20 bolt which has an external 7/16" thread, which could be tapped into the hole in the backing plate and epoxied in place. Then I'd theoretically be back in business, once I fill the enlarged hole in the glass back up. But I'd rather go the other route, if possible. I'll let you all know how it turns out. Thanks for all the great brainstorming. This forum is great!
Peter