Based on my own experience I would suggest that you can sleep fine in an uncomfortable situation until you're in a light enough sleep that you'll wake up.

The rested feeling is simply not waking up in the middle of a deep sleep cycle when your body is flooded with melatonin. Alarms simply don't way us up optimally. They blare at us with no regard for how deep we're sleeping.

I don't think either extreme, sleeping uncomfortably or fighting with an alarm, is the answer. There's an interesting alarm app on Android phones that will ring quietly x amount of time before the real alarm is set to ring to see if you're more awake then. I'd like to see more attempts at hybridization like that.