AKo brick 4bet flop with initiative 1.5:1 SPR

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AKo brick 4bet flop with initiative 1.5:1 SPR

Blinds: $0.01/$0.02 (6 Players) BN: $2.64
SB: $3.83
BB: $2.00
UTG: $3.17
MP: $2.06
CO: $2.00 (Hero)
Preflop ($0.03) Hero is CO with K A
2 folds, Hero raises to $0.06, BN raises to $0.18, 2 folds, Hero raises to $0.48, BN calls $0.30
Flop ($0.99) T 8 3
Hero

Opponent is unknown.

I assume his range to be pretty much TT+,AQs+,AKo.
Bet/call is no option as he will have at least TT+,AdKd,AdQd against which I have 21% equity, i.e. I'm loosing a quarter stack in expectation.
Not sure it's worth bet/folding out (or if he even does fold) hands we are chopping with.
Check/calling makes no sense as I don't even have a bluffcatcher.
Check/folding seems weak with initiative in a 4bet pot.

In position with the Kd I would probably want to see a turn and check back, but oop I have absolutely no idea. I'd just c/f..

Are there any standard lines here? Should I avoid getting in these spots in first place by flatting 3bets oop against a wide 3bet range and disguising my hand/outflopping him?

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