The stuff's pretty much gone now. Cleaned it off my hardware and most of the decorations, scrapped some live plants that were heavy with it just to cut the volume of it down, and did a couple more water changes and a thorough gravel vac (seemed to be a good bit of it in the gravel, too), and removed all my driftwood and boiled it (driftwood is laying out to dry right now).
Whatever it was didn't seem to hurt any of the fish - it never attached to them, and the otos even ate a bit of it, and didn't last long (though I'm not entirely sure my apple snail is well, he hasn't come out of his shell much in the last couple days and had a good bit of it sticking to his shell which I rinsed off in tank water). I'm thinking it came from the driftwood, which I've had soaking for quite a while while I prepared the new tank, but that didn't produce anything like this in the bucket.
I did a lot of googling yesterday and today, and I think it might be some kind of water mold, which would support my theory that the driftwood was to blame. Shouldn't boiling it when I got it have killed any of that, or is it possible I didn't boil it enough?