If the BB likes to steal then a small 3bet-fold is fine. If not I prefer flatting pre and tending to fold the flop.

Why are you so eager to gamble so many chips, when you have a nice stack and a non-premium hand? You can afford to wait for a better spot.

I think it's prob close btwn 3bet/call and shove. OP didnt provide any reads on btn but he did say that he (OP) had been 3betting a lot in this tourney. It doesn't really matter if ur resteal 3bet is 85% if btn hasn't seen any of ur 3bets. Reads on the BB would help too. If ur main reason for choosing a std 3bet size as opposed to a shove is concern about BB waking up with a hand, then ur prioritizing your variables in a really suboptimal way.

If ur gonna 3bet/call then I think ur 3bet sizing is fine. You're way ahead of btn's opening range and there is a lot of value in folding-out the weaker portion of btn's opening range with all the dead money in the pot. When he reshoves you're getting 1.78 to 1 to call, which means u need 36% equity to b/e. KQo (aka Stars Nizzles) has 36% vs a btn range of:

55+,ATs+,ATo+ (which is the 'value' portion of his range.) If btn perceives that he has a decent amt of FE then his range can expand (and our equity increases) significantly, at this point folding becomes a mistake.

A smaller 3bet size (~3500) is prob ok too since btn really doesn't have enuf chips to peel. This sizing will induce shoves from a wider range but it also increases your variance. For example if btn opens 40% of hands then Ax (where x < 10) makes up a big portion/30% of his 4bet bluff-shoving range, which is not good when we hold KQ.

Shoving 24bbs eff is obv cEV+ but there has to be a threshold where shoving over a minraise becomes less profitable (than 3betting to a std size.) We can always formulate ranges then compare the cEV of shove and 3bet/call to see which is more profitable.