This is kind of a long short, but last night I finally figured out the security question, and just as I solved it (right after the heart piece appears), my game crashed back to the game library. I reloaded, hoping the auto-save had happened in time, but no dice -- I solved the puzzle again, and it crashed in the same spot. Third try, third crash. I've only got 2 cubes to go, and I'm nervous about further glitching and/or losing my save, so I figured I'd stop playing and see if anyone else was having the same issue (and if there was a known workaround). I've emailed Fez support, but I imagine they're pretty swamped and don't expect a reply any time soon haha.
P.S. Amazing game, eh?