this might not be the answer you want but the math and science behind decisions like these are derived from bayes theorem and super complicated:

https://en.wikipedia.org/wiki/Bayes%27_theorem

obviously the 3bet vs UTG maniac is +ev since you have the hard stats to prove it, but it gets tricky to assess the btn since the prior information you have in this spot is that he is an aggressive reg which is very undefined

so the bayes theorem calculation here is whether this player is adjusting by widening 4bets or just 4betting regular with some default 4bet range

im not too versed with the actual bayes calculation because its way more difficult as opposed to learning about it in theory, but in the end you get a distribution of true/false positive/negative results

my intuition based on little knowledge of bayes and poker theory tells me even if the reg is adjusting, once the utg flats were in a new spot where we need to recalculate everything and even at that point A9 is just an poor hand to jam unless a series of very exploitative conditions are met (block 4bet, btn 4bets K/Qx and small pairs, UTG both raises and flat wide, some fold equity, etc.) and on top of that being torn on whether we merge or polarize jam here

"with the 9 unblocking some weaker cold4bets."

I think you're trying way, way too hard...in general you should not make enormous adjustments based on vague notions that someone might be adjusting, especially when your play still might not be good if he is in fact adjusting (he may well 4bet a bit wider than normal but you need him to be very out of line for this to be good)

It doesnt really sound like theres much of a plan to this hand. Why are we 3betting? Why are we shoving? Why do you think theres dead money in the pot?

We're shoving because i expect to recieve an undefined amount of folds from both players while still having decent equity when called. There's dead money in the pot because the maniac coldcalled the cold4bet, presumably with a wide range. Assuming we have 29% equity when called by one player the indifference point would be roughly 40% folds.

Honestly i think 4bet from BTN is really strong here. Maybe they are adjusting, but you'd need a fair bit of evidence and a good idea on range to justify this shove. I think you're probably owned equity wise. 3Bet is totally fine, but the BTN 4betting wasnt part of that plan so just let it go and move on