Waiting for a safe river

[Knet]

I don't run into this situation online much, but when I play live at my local casino there is no cap on the 10/20 NL game so the stacks are usually much deeper.

I know that there are plenty of situations where it is correct to wait for a safe turn card before you make your push, but is it ever correct to wait for a safe river card?

Example:

Effective stacks are $4000 and you open in LP to $80 with 52s and get one caller from the blind. The flop comes A43r, you bet $120 and get called.

Turn bring a 9 completing the rainbow, you bet $300 and he makes it $1000 to go. At this point you are almost certain the villian flopped a set bc he would 3 bet OOP with a strong ace and fold almost all other hands with an ace. Caling would have about 120 BBs in the pot (leaving 140 behind for each).

Is it always correct to 3 bet him here? If I started the hand with 100BBs then its an auto-push bc I don't have much left. Howver if we are deeper things change a bit. This is a pretty dry board so the river will most likely not slow him down, and since there is always a chance the villian is running a bluff we can call and let him continue. How do you play a hand like this? How does your decision change if:

Effective stack is 300BB?
Effective stack is 500BB?
You are OOP?
If there is 2 of one suit on the board?

I threw in the last one bc the river has more "scare card" potential.

I know I'm a new poster so sorry if this question is bad/dumb etc. This is just something that I have been struggling with since I started playing live more, online the effective stacks are usally 100BBs so when a rare hand like this occurs (dry board, hidden hand, against a easily readable player) its even rarer to happen when the stacks are deep. It just seems that there times you should wait til the river to make a big bet and get 100% equity instead of 75% equity on the turn

Thanks for any comments.