Hi all, thanks for your excellent advice. After riding some more this weekend, I decided that the 20" frame is the right size and going to 17.5" will probably be too small. By looking around town at other "more pro" riders, I have noticed that their bikes have a similar fit to mine: when sitting, the toes reach the ground, but the entire foot does not lie flat, and they simply hop off and forward from the seat when fully stopped.
Just to correct my original post: When I had the Schwinn, it was actually the entire crank-arm that fell off. Probably not a fault of the bike itself, but of its poor assembly. Having this happen with only two days of riding definitely tarnished the Schwinn experience.
The Trek 7000 comes with the Shimano TX rear derailleur, which is very cheap, cheaper than the Shimano Altus the Schwinn had. I'm surprised Trek wouldn't at least have a better derailleur, so I'll probably end up replacing it in the future.