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with 7 BB total between you, what you do makes absolutely no difference once you get past third and not getting it in on third is criminal.
The structure is seriously whack at this point, but are you saying hero has no choice but to essentially push on 3rd just after the completion? Once it's 3 bet I agree the die is cast, but it certainly reasonable to flat call 3rd and still be able to fold 4th if the cards break horribly. Hero is certainly ahead of villain's range with random hole cards, but just because hero wants to play for stacks doesn't mean villain has to go along with it. He can flat call or even fold to the raise on 3rd with his worst hands and only play for stacks when he's ahead.