I've ruled out getting a fixed-gear bike. While it would be awesome to be able to slow down while riding no-handed, the fact is that it's extremely rare for trials or BMX bikes to be fixed-gear. They're almost all single-speed.
And the reason seems clear enough — a lot of the time you're doing tricks, you're out of your seat. When you're starting to charge up the wall of a vert, you want to be as stable as possible, and preparing for the moves that your trick requires.
Having to pedal while you're out of your seat makes you less stable. And having to think about pedal position in ADDITION to all the other stuff going through your head when you're setting up for a trick, makes it that much harder.
That isn't to say it can't be done. Unicycle trials is rarely (never?) done with a freewheel. But unicyclists don't do vert.
The fact that BMX/trials bicyclists have settled on single-speed means that's the way I'm going to go for now. I'm a neophyte, and this seems like one of those "you have to learn the rules before you know when you should break them" cases.