Apparently people have downgraded systems from testing to stable using APT, but this sounded tricky. Just changing the sources list and doing dist-upgrade doesn't work, and apparently people who have done this have to pin a bunch of packages and somehow fool it into downgrading. Given that most of the info Google turns up on this is seven years old, I didn't want to risk it. Normally I'd just do another install into a spare partition, but having had such a smooth ride with Debian for so long (I ran the same install for something like five years, until finally moving on to 64-bit), this is the first Linux machine in years I didn't bother making such a partition on.
Instead, I installed Debian stable into a subdirectory (/lenny) using debootstrap, chrooted in to install packages, and prepped the /etc directory. Now I was ready to switch systems. I got the statically linked version of busybox and, while still in X11 with music, Firefox, and IRC going, did the following:
lightworks:/# mkdir sqeeze
lightworks:/# mv bin emul/ etc lib lib32 lib64 sbin usr var squeeze/
lightworks:/# cd lenny/
lightworks:/lenny# mv bin emul/ etc lib lib32 lib64 sbin usr var /
Now I'm running Debian stable. Everything is working just fire, except I had to restart firefox, and install some xfont packages for emacs. This is one of those rare instance where I'm genuinely pleased with my operating system. There's some loose ends to tie up, like configuring X11 (I'm still running the one from sqeeze; I'll fix it next time I quit X), and some miscellaneous packages to track down, but at this point I think I'll declare this stunt a success.