Yes, I did try flashaid. It's a great extension and I've used it to good effect once before. But this time, the URL that's hardcoded into the script goes to a page Adobe moved or deleted, so the whole script fails. Very annoying.
I also tried renaming .mozilla (to .mozilla-bak) and letting Firefox recreate it, but it still can't detect the flash plugin.
Which is interesting. What that suggests to me is that the problem is not in my ~/ config or profile files. Also, the plugin files are in /usr/lib/mozilla/plugins and symlinked in /opt/ff14/firefox/plugins. The first is supposed to be the standard location, I think. (Right?) If FF was using an absolute path, it should find it. This must mean FF is using a relative path to a directory somewhere among the system directories, one that can't handle the extra nesting caused by my ff14 directory.
Firefox could make everyone's life a lot easier if they TOLD us where this magical location is, and standardized it, and kept it consistent between versions, and let us know where, exactly, we could install firefox when doing it manually. (Grump, grump, grump.)
Anyway, I'll check that theory by putting firefox14 in /usr/lib/firefox and see what happens. Wish me luck.
(By the way, the other alternative besides Chromium or Opera is to go back to my good old FF5, which is what I did.