The job is done! Everything is back together and works fine, nice fat brake feel and the pads are breaking in nicely. Thanks to all for your advice and counsel, it was a matter of just deciding to get over the jitters and do it myself. For future reference, if you are unlucky enough to shear off the rear brake caliper bolts leaving the stub in the axle housing:
1. Go have a beer, berate yourself, bemoan your fate, but know that this too shall pass and there is a way out. Just work on it later.
2. Go after the stub from the front not the back side. You’ll have to remove the parking brake, the brake shield and pull the axle, but it really doesn’t take that much time and it makes a clean extraction possible.
3. Go buy a cobalt drill bit and an ez-out. The cobalt bit will cut the grade 8 bolt material like butter and having removed the axle you have the clearance to use an ordinary 3/8 drill motor to drill your hole straight. Go after the remaining bolt material with the ez-out from the back side.
4. Didn’t work? Read all the other advice about heat, using a chisel, etc.? Material still stubbornly in the hole? Don’t worry, go back and get a bigger cobalt bit (3/8) and clean out the remaining material. You can easily retap the hole to 7/16.
5. My method:
a. Drill a 7/16 clearance hole in the brake caliper. Use a drill press or trust to luck if you wish. I used a press because I was afraid to get the clearance and tapped holes misaligned, ie. I’d be able to get the bolt in but not threaded. Just be sure your hold is centered as best you can. Take it to a machine shop if you are unsure.
b. Drill the hole through the axle using a .3680 jobber bit. Check with your local bolt expert for the right diameter for your oversize bolt.
c. Mount the drilled caliper on the axle and line up your holes. This is the point where you will assure your new bolt will actually fit.
d. Tap the axle hole (from behind, facing you. Figure out which way the bolt will tighten and turn it that way to cut the threads) using the clearance hole through the caliper as your guide. This will ensure that your bolt will at least mesh with the threads you cut when you reinstall the caliper.

Everything mounted up tight and seems to be OK. A real nail-biter until I figured out what needed to be done. Thanks to all for your help. ‘til next time, bj.