Given the complexity of this hand I think you have to fall back on a plan that keeps it simple (after all the analysis over a couple of days there's still not an obvious conclusion): try to play a small pot but attack weakness. Check the turn and push all-in check raise if he weak bets the turn (representing AK), check the river with the plan to call any reasonable bet (he's likely to sell it to you here after the previous action since he has no reason to believe you'll pay off a big bet).

I think you played the hand well - I'd rather be kicking myself about some marginal value bet I could have gotten (maybe) on the river than doubling him up.