1/3 NLHE - Multiway 3bet pot spot with AA

I don’t really have experience w multiway 3bet pot spots and pretty much acted out of fear leading to misplay

Hero is 1k effective, tabled turned gutshot bluff in 3bet pot earlier

utg raise 25

hero in co 3bet 100 w/ AA

btn straddle (sweaty reg) and utg (young/solid) call

flop K79r

utg check

hero cbet 100

btn and utg call

turn T (suit = two-toned board)

utg x

hero (??)

My thoughts: >!Don’t really have too much to say abt this. Couldn’t figure a range for each person besides Kx and middling pocket pairs that would flat a 3bet multiway. Figured I don’t have a good chance to get QQ/JJ to call one more street. Tried to target sticky Kx here, ended up jamming for my remaining stack. Don’t have a good reason why as I’m beating everything under the sun besides some 2p and sets, just thought bet-bet-bet wouldn’t work given this config. Turn x likely will x through. bet-x-bet also lets btn realize the river for free. bet-bet small-block could’ve worked better. Looking for y’alls thoughts!<