[chisness]

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I would make a smaller raise on the flop to make it look like you actually have a set. Or call flop and reeval turn. Shove screams big draw which means overpair calls

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If you call the flop and reevaluate the turn you are not guarenteed to get action on a king/spade and will most likely face a turn bet. So I think calling the flop would be bad here.
Okay to adress your 2nd point, I doubt someone folds to a small raise on the flop but calls a large overbet push on the flop. Equity vs his range when called on the flop is pretty good. It is bad when you make a small raise and he flat calls flop, you lose value by getting the rest of stack in on the turn with only 1 card to come, ehh?