IMO thats the perfect line. You have to raise the flop with that monster draw and hope he has something to pay you with. Pushing the flop is out of the question even after the raise, he only calls with a set or top-2 IMO but i wouldnt put him on top 2. You definetly cant check the turn, you're throwing away huge value and letting hands like AQ off way to easy, and with 12 outs minimum, and 40% of your stack in the pot I dont see how you cant make a strong bet there, you've shown great strength thus far and its definetly a +EV move.