Okay, I feel like even MORE of an idiot.
The FTP layer is not enough to drive Community Builder. When setting all the appropriate directory permissions manually to 777 (per the Joomla System Info page), the fields started working.
See also post RE SEF with Joomla Article Sharing:
www.jms2win.com/forum?func=view&catid=26&id=2533#2533.
Anyway, totally my fault I guess (definately not this component I now LOVE and cannot live without). I did not see an explicit item stating that the base site needed to have the permissions manually set in the documentation, but you probably assumed people aren't as dumb as me when it was written.
Still having some mootools JS issues and conflicts, but that's a different topic.