It seems to me that the way a task is framed greatly affects how much willpower it requires.

Yes; I can't remember which overcomingbias posts it was in, but Robin Hanson has floated a theory that willpower is a hack whereby, for social reasons, we override our natural and correct (in the EEA) instinct. Obviously, it doesn't pay to make such an ability infinitely strong; people who go on hunger strikes to make a point have few offspring. So, a task framed as something useful in the EEA would require much less willpower than something framed as socially praiseworthy, but otherwise harmful.