Thanks all... What I realized was that FLV wasn't what I needed; it was SWF. I'm suddenly not sure what FLV is actually used for.
...and with that in mind, I found that Flash Video Studio (
http://www.flashvideostudio.com/) is what I was looking for. I can hardly believe how good this app is (I've gone through more video converters than I can count on all my fingers): it reliable, doesn't have annoying size/ratio/etc limitations (like most the other FLV converters I tried - might have something to do with the fact that it uses SWF though, not FLV) and even has a small library of player skins that you can edit.
The only drawback (with Flash though, not the program) is that you're limited to 16,000 frame movies (in SWF format, not FLV though), and my movie, quite naturally, is longer than that.
SO... anyone know of any good QuickTime converters? I want something that will play nicely in a browser, with a nice-looking player, but I'm talking about 40 minutes of footage here: not something SWF files can support. (16,000 frames??? How did Stage6 do it?)