If you're comfortable flipping with pocket pairs at the final table, then just go ahead and jam with AK.
There is no information, that this was the final table. And even if it was, our range should not change much, as long as we have fold equity. Which we most definitely have by rejamming a 20 BB stack over a min-raise. Even the final table is not only about trying to fold our way to a small payjump. Its also about accumulating chips and trying to make a run for the top 3 spots. This is where, most of the profit is won or lost in MTTs long term.
Otherwise AK doesn't really play well against several players.
Which is part of the reason, why we rejam. We hope to either get everyone to fold or get it in against one opponent at most. And they will not always have a pocket pair. People do also regularly call with dominated hands like AQ or AJ. Or hands a lot worse than that, since this is a freeroll, and a lot of people dont even try to play well.
Or you could just fold your AK.
I assume, you mean to the cold 4-bet from SB? A cold 4-bet is very strong, but the issue is, Hero had already put in more than 1/3 of his stack. He had to pay another 31k to win a pot of 107k. This mean, that even if SB showed Hero pocket kings, Hero would still have to make this call due to pot
odds. And against JJ it was a massively profitable call, which just did not work out this time. Only if Hero was shown pocket aces, could he get away after 3-betting. Which is why, a 3-bet should be a jam with stacks this shallow.
I know it sounds nitty, but you're out of position
Hero had position on both opponents, and positions dont matter, when you are all-in, since there is no more action to come.
and you may have better hands down the line yet to play from better positions with almost 20 BB behind you.
You dont find many spots in poker, that are more profitable than being able to rejam AK with a 20 BB stack. Such spots print money in the long run, and they allow you to build a big stack, which you can then use to pressure other players and survive future coolers and bad beats.
Personally I don't go crazy with AK (especially offsuit) until I am down to close to 10 BB.
Thats a big leak in your game.