I think your read appears rather contradictory. You state he is irrational, yet he won't call with a big pp. I doubt his that weak, and given the apparent weakness you've shown throughout the hand I think it's likely he'll call with something like KK or QQ (his most likely holdings IMO). This leads me to bet/fold here, as I believe he'll call with more hands than he'll bet. Assuming villain is capable of bluffing the river or betting with a weaker hand.

However, if we believe villain isn't betting a worse hand with enough frequency relative to the pot odds, then I'd suggest check/folding. Though, you gotta be pretty confident in your read here.

Personally, I think check/calling is the worse option, and the only line I wouldn’t consider.

Overall, I think it's highly read dependant.