[Nate tha' Great]

The whole play of this hand is so strange that I can't see myself folding for one more bet.

Here's another solution: bet the river. If he raises you, you can make a determination as to whether it's best to call down or 3-bet based on action tells. But folding is out of the question unless he turns his cards face up. I know that you take pride in your ability to make tough, situation-based reads, but I don't think you've got enough information to go on here.