JJ facing 4B

Doesn't strike me as a situation where positionally or stack/bet size wise the villain ever has any bluffs and likely his 4b value range is AK+ QQ+ so I think you can just fold now

Pretty easy fold. QQ would be more interesting

Probably correct. Knowing stakes and whether this is live or online might shift that range, but this deep I suspect by and large just folding is going to be correct.

Based on this which I agree with what do we get it in with

KK and AA with some potential to actually restrict ourselves to AA vs some?

Ultimately he probably has some AK here but he has a lot more QQ KK and AA

I think its an easy fold. If UTG has AK he would more likely jam than play this OOP against a PP like QQ/JJ.

His 4bet is close to 40% effective stack assuming one of the callers has a larger stack, otherwise it is 50% effective stack.

AA/KK. QQ and AKs are around 41% equity here which is not quite enough to put our stack in (we need 42.7% to break even, to put our 18,400 behind into a pot that will be 24,660 when our 5-bet shove is called).

Maybe I'd shove AKs sometimes if I thought he would fold QQ to it, since that's a significant part of his range when we have AKs and we'd pick up a huge pot.