The very pleasant experience at the Genius Bar (Apple Store, West Hartford, CT) resulted in a new replacement phone. I know all the homework helped. When I scheduled the GB appointment, I included my last post here (slightly edited, with all the links). I knew what I was talking about.
I went in with the Wi-Fi network settings screen on to show the constant find / lose of the Apple "Store" and "Demo" networks. He then did a network reset and said, "There. It's working." I said, "Give it a minute" and twenty seconds later the network disconnected. He asked me, for the record, if I tried the full reset, etc. He then asked, "So you'll be OK with a replacement phone?" The whole process took 15 minutes.
The longest part of the process is done at home: restore from backup, iTunes resync, etc. (Interesting to me how this is not completely intuitive. The initial restore only restored native apps since I hadn't connected this phone to my iTunes account.)
For those who are under warranty and lucky enough to get to an Apple store, I think if you go in with a positive attitude of understanding and have done your homework, you should have a good experience. Out of warranty, your mileage may vary.
Good luck.
PJI
PS. The G at the Bar told me he hadn't really seen this problem. Again, this leaves me to believe there is a specific lot of phones with this problem.