Props to villain for wizardry. As played, I'm in the 'get exploited and fold river' camp too.
However unless we are perceived as maniacal, I think the river is a check.
When we call the raise on the flop we have very few river bets that can get called by worse. What is our perceived range when we bet/call, check, lead on this runout? Seems pretty strong to me. What hands does villain have that he will call with vs. our range?
I'd expect villain to have far more value-owns/bluffs than calls in his range with his line. If we check river, almost all the hands that we are trying to get called by are going to value bet themselves.