A third possibility: Humans aren't in general capable of accurately reflecting on their preferences.

Humans are obviously capable of perceiving their own preferences at some level, otherwise they'd be unable to act on them. I assume what you propose here is that conscious introspection is unable to access those preferences?

In that case, utility functions could potentially be deduced by the individual placing themselves into situations that require real action based on relevant preferences, recording their choices, and attempting to deduce a consistent basis that explains those choices. I'm pretty sure that someone with a bit of math background who spent a few days taking or refusing various bets could deduce the nonlinearity and approximate shape of their utility function for money without any introspection, for instance.

A third possibility: Humans aren't in general capable of accurately reflecting on their preferences.

Three is pretty much like one. If utility functions work, there must be some way of figuring them out, I hoped someone figured it out already.

If utility functions are a bad match for human preferences, that would seem to imply that humans simply tend not to have very consistent preferences. What major premise does this invalidate?

Utilitarian model being wrong doesn't necessarily mean that a different model based on different assumptions doesn't exist. I don't know which assumptions need to be broken.