I think we can figure our hand to be good the majority of the time, but given the scary board we want to get to showdown as cheaply as possible. I would 3-bet the flop, and check behind on most turns, especially with the 4 on the turn, and plan on calling a river bet. If he caps the flop, then i fold UI on the turn.

Although, calling down is not bad either, because this seems like a very aggressive opponent who may just be trying to run you over.