What do you think? Would you gii preflop, even though we're 150bb effective?

I think we just have to get it in pre. Even though its 150BB effective. Its blind vs blind and as long as you are 3 betting a solid amount his 4 bets could definetly be pretty wide OOP.
If he is 4 betting JJ+,AKs,A5s-A3s,AKo you have 64% equity but you are put in a tough spot like you were above if he is aggressive. I think you should 5 bet jam. If he only continues with KK+ he would have to fold 81% of the time giving us an EV of .81*17.76= 14.39. We would have 20.5% equity when called with an EV of .205*29.3 = $6
We would make 14.39+6-14.65= $5.74 in EV.
If he calls with QQ+ AK he would fold 38%. You would get .38*17.76= 6.75 when he folded.
You would have 57% equity when called with an EV of .57*29.3 = 16.7
Here you would make 6.75+16.7-14.65= $8.80 in EV.
Even if he only 4 bets QQ+ and only calls with KK+ he will fold 37%
.37*17.76= 6.57. When called you have 20.5% equity .205*29.3= 6
6.57+6-14.65 = -$2.08. If you have a specific read that villain is doing this then you can exploitatively fold to his 4 bets without AA( but I wouldn't sweat getting in KK) and 3 bet him extremely wide.
If he 4 bets QQ+ AK and continues with KK+ you are also profitable.
This is a very high variance spot but you cannot stop yourself from shoving because "He always has aces".
Even if his 4 bet range is not as wide this will be a profitable shove in the long run.

Haven't gone through the maths of above post as it's abit over my head , but pretty much agree with the first 5 lines.

There are several mistakes in the actual EV calculations here, but I agree that the conclusions drawn are still applicable.