I agree that shoving over the flop minraise is the best play, but not because we have any leverage or fold equity. It's the best play because this is what we wanted when we 3-bet a 1/2 stack pf. The hand pretty well plays itself once the flop bet is made.

I guess in this scenario, if villain does fold a draw, that is probably better for us, because he would be giving up a fair bit of equity.