I'll bet this on the flop and hope the aggressive BB raises me. I don't want gutshots and OESDs calling, and charging flush draws and OESDs is great.

On the turn, your kicker doesn't matter anymore, as the A-K kickers are shared with any Q. You are dead against AQ and KQ, and slightly behind AJ and AT (as they have freerolls against you). I think I go to town on this turn, expecting to split with a Q most of the time, and see a straight or ace some percentage of the time. I don't know why you're waiting until the river to c/r.

River is fine.