I put the new timing belt on today and it started up! It made a horrible noise and cylinder #1 had a problem - it was running like an exhaust valve was stuck open. But after letting it warm up I slowly revved it to high RPMs and then it ran fine again. No problems yet. Yay!
So I think I got the whole interference thing figured out. Honda does label their engines as interference engines, but:
"Given that, in reality the Honda engine isn't a "true" interference engine. They gave just enough clearance between the valves and the pistons that, assuming there's not a lot of buildup on the valves, you won't hit if the timing belt breaks. That's a really big assumption, and Honda is afraid of lawsuits: if someone was running an ill-maintained, crudded-up engine that Honda claimed was noninterference, broke the timing belt and bent four or five valves, their first stop would be a lawyer: "But they SAID it was a noninterference engine!" They cover their asses by claiming the engine is interference. This way you can be happy if you break a timing belt and not bend any valves, and you won't sue if you do bend a few."
This may not be true for all Honda engines, but it makes sense.