The floors climbed uses a mixture of the altimeter and arm motion (that way it doesn't count floors when you're in an elevator for example). It's quite likely that having to go up the stairs on your butt using your arms is both very slow and not swinging your arms enough to register as movement. While I can understand the frustration it's hardly surprising that the watch can't handle this - you're talking a very specific scenario that if Garmin tried to capture would probably result in "false-positive" floor climbing readings for the vast majority of users. I hope you have a speedy recovery from your injury.
