I like your shove because at these stakes some players just can't lay down 4x, not to mention a flush or straight.

Normally though with such a strong hand I would raise the flop or turn, even if we're not bothered about protection. On the flop we're now heads up and it's easy for him to put you on a bluff,plus you get added value from flush and straight draws. Also players will tend to believe river raises more often than those earlier on, you will get called lighter than you expect a lot of the time.

I would have liked a raised on the turn as I think Ax doesn't fold neither do PPs. The only hands that do fold are high card hands like KQ which we was never going to get value from in the first place.

As for the river, I like making it $4 than shoving as we're rather deep and they will fold overpairs that will call a smaller raise.

Raising flop is better than raising turn for very obvious reasons. We rep draws more often and get value from draws also on the flop plus it builds us a pot so we can bet bet bet higher amounts and get 3 streets of value.

I'd probably go for a raise too on the turn, but I'd make it decently small, wanna get more money in this pot. 4x has a FH so we don't expect fold from them. I don't hate the shove though.
But we can just make a decent raise I think, as pointed out above. Since we're deep, they need a real good hand to be calling.

We can also raise flop as we don't often get respect here and also there are a lot of overpairs which will feel too nitty to fold.