I would never shove this on this stack depth as there are bigger stacks then ours already in the hand so we have the effective stack (from our perspective anyway) of 57 BBs which is way too deep to jam AK or probably any hand for that matter since if we had a made monster here we would not want to jam where villains would then fold their 99 ish possible hands.
Its true, that we are the effective stack with 57BB. But how often does BTN or SB have a hand strong enough to call us, if we jam? 99% of the time they are just in there trying to setmine, or they have some kind of suited connector or decent broadway, which looked to good to fold, but was not good enough to 3-bet. So the only player in this hand, that really matter, is MP, and against him we are 45BB deep.
Admittedly this is still very deep, and there are probably not many hands other than exactly AK, we would want to jam for 45BB in this situation. But does this really matter? Even if we showed them AK after jamming, what exactly are they going to do about it? They still cant call us with their QJs or their 55, especially not those, who still have people left to act behind them.
Occationally we will run into AA or KK, and thats going to suck. But if we 3-bet small, we are still not folding AK to a 4-bet with these stack sizes, so running AK into KK or AA is just a cooler. And if we get called by any other hand, its not a bad situation for us, especially not with some dead money in the pot and bounties to fight for. The value of building a big stack is also larger in a PKO, because it allow us to better contend for bounties in future hands.
I would go with a passive route here and call and then depending on villains post flop call frequencies, we can make the pot large post flop when we want to and then also fold cheaply when we dont hit the flop.
The issue with calling is, that AK dont play particularly well in multiway pots. Yes we keep some hands in, that we kicker dominate, and thats great, when the flop comes K73, and someone else has KQ or KJs. But its not so great, when they have 77 or 33, and we need to remember, that BTN and especially SB will often have setmine heavy ranges. If we call, the SPR will be around 5-6, and thats right in that grey zone, where it can be really difficult to figure out, what to do with a TPTK type of hand.