I dont like the min-3bet. With AA (or high pairs generally spoken) you better push Equity as much as possible. The $-amount utg+1 calls and possibly fold on the flop is pure and easy value! Another effect is, you isolate him. As played other players behind you join the pots making it a small spr pot oop multiway. This way it is harder to get it in against utg+1 on the flop because there are still 2 players left to act behind you which you have to take care of.

On the flop with trips-top-kicker you hit the virtual nuts considering that 22, 42, 44 are not around in this spot normally. No need to balance here, the spot is uncommon and multiway. Just go ahead, play it fast, valuebet/push out potential flushdraws or trips behind you and bet full pot and double-barrel pot on any safe turn.

I think the min-3bet is fine. It´s player dependant, but I think most of the time he won´t shove and you´ll be missing some EV. When he shoves though you´ll get a lot of EV.

Flop and turn I don´t see any reason to not bet. I think you´ll have the best hand more than 80% of the time. Just bet/bet/shove for value if the river isn´t a flush completing card.

I´m not saying he is folding against a pot-sized 3bet. It´s just that some other players might get trapped in a sandwich after they call PF like this guy on BB that would be leaving at least 7 extra bbs in the pot or someone could even 4bet a hand like AKK, AKQQ, idk.

That said, I´m not sure about this play though. Just saying it is worth considering especially when the original PFR is a maniac.