$50 plo 3b pot with AKQTds, flop options?

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$50 plo 3b pot with AKQTds, flop options?

BN: $54.78
SB: $158.06 (Hero)
BB: $143.59
HJ: $71.58
CO: $54.29
BTN = 54/32/17, rather spewy
HJ = 26/16/9, reg
BB = 23/12/4, kind of TAGish reg
Preflop ($0.75) (5 Players)
Hero was dealt A K Q T
HJ raises to $1.75, CO folds, BN calls $1.75, Hero raises to $7.50, BB folds, HJ calls $5.75, BN calls $5.75
Against HJ open and BTN flat this seemed like a good enough hand to 3bet, although we would hate to get 4b by BB. By any chance, is it okay to flat here too?
Flop ($23.25) 8 2 9 (3 Players)
So we flop rather okayish without hitting a pair. SPR is about 3 vs HJ, and 2 vs BTN. This probably hits BTN's range the hardest, so if I and HJ check here I expected BTN to take a stab quite often. At the same time, if I check, HJ pots and BTN shoves I might be able to find a fold, as I might not have good enough equity vs 2 strong ranges.

That said, what would be our best option? Pot/call, or x/jam? Is checking too dangerous because BTN can just check back so often?

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