This may be a stretch in and of itself - but could your rear wheel become loose in the dropouts and cause the tire to rub on one of the stays?

This is really odd. It only does this when you are applying pressure? Something has got to be rubbing something. I'd check it again on your repair-stand. Get on it an pedal gently while trying to shift from small to large up front. Then if/when this happens - stop and get off the bike. Now - got a flashlight? - take a look to see if the rear wheel is rubbing something.

EDIT - Which side did it fall on? Derailleur-side or non-drive side? Another candidate I'd look into is your gear-shifter.