Thanks for the suggestion. I DID think about that a little, but I have three worries, in increasing order of concern: (1) I don't like the idea of removing any structure as I drill for the larger size bolt, (2) the nut (if that's what it is!) is quite deep in the hole, so I might need a quite long tap, and it's not clear how much space there is beyond the nut for the tapered part of the tap to go, and (3) tapping stainless is no fun, even with lots of cutting oil, and if I break off the tap, I'm in REALLY deep trouble. It's possible that I'll still end up going this route, but as you can see, it makes me a bit nervous.
--John