Finally. Sarissa did indeed ease my XML suffering; thanks for the pointer,
jaq! Lots of other hangups to overcome, but nothing that stumped me. Much was learned.
Here's the same boring old Tic Tac Toe demo which works in MSIE (and, afaik, everywhere else) now, and
here's a zipfile of version 0.2. Everything's up to date in Subversion.
Now that that's done I will stop seeming to obsess over this one example and start making some more interesting prototypes. Much of this suffering was done over JavaScript library code, so it should all carry into the future nicely.