In another (hopefully temporary) retreat, after exhaustively testing tornado-redis' connections and deciding that either I utterly fail to understand them or they Just Don't Work, I ripped them out and went with the standard Python redis library. Which, of course, works like a charm. Go figure.
Also in failure news: redis recommends a protocol called Redlock for transactional writes. Unfortunately -- you guessed it -- that doesn't seem to work either. So that's another (I think the third) kind-of-big-deal try-it-again-later point that's come up. Which sucks, kind of a lot, but at this point I just want to move forward.
The good news is that the current arrangement, while I would [i]not[/i] call it ready for prime time, does work and is still blazingly fast.
Since this is "done," the next thing I'll do is start actually teaching the server and client to exchange interesting information (phone numbers, turn-ons, turn-offs, etc) for details and listings. Much more interesting!