Q is not good card for you on the turn. We should check. If he checks back we can jam a blank river for value. 1/3 pot on the turn isn't terrible either.
The real sick thing imo is if we check and he bets $500 and then he jams a blank river. Hard to fold, with what is left behind.
I think our preflop and flop sizings are a bit large. I would prefer going $120-$130. 4-4.5x +1x for each caller, which would be 6.5x. You went 7.5x. When we are OOP at 300bb deep and the initial raise is already 4x the bb I am not a fan of sizing up that big.
Flop I also prefer 1/3. On the flop and we can definitely have some checks top protect a checking range here.
It's generally hard to get away from a hand like TPTK or an overpair as the OOP 3bettor, but here we are starting the hand 300bb deep. We don't have to set ourself up for situations this deep where we have to stackoff with 1 pair.