The drill/tap/screw idea isn't workable - there's an additional tab to go through to get to the joint (sticking out in the photo). I guess you could do a larger hole through the tab for the screw head to pass through, but there wouldn't be much material left.
Well, the first round, gluing just at the break, seemed to hold very well, so I just added another layer to completely fill the gap around the joint. It's curing right now, will shape and paint later today. Heading out of town for an overnight trip, so I'll report back late tomorrow. A new mirror is only $72, so no big deal if it doesn't hold.
PS: JB Weld would have worked just as well, maybe better.