you rarely if ever have your Ace pair outs (-3) and very often you are up against other flush draws, sometimes having Jxcc in their range.  i would say that even for the sake of argument if you are showing a profit from a chip equity stand point you should probably let it go in terms of having a potential tournament strategy edge over the table. from the sounds of it you have the big stack to your right and some inexperienced players to your left.  preserving your 34-37bb stack is going to be pretty crucial here in picking up chips the easy way later, as losing this pot would put you at push/fold (not an ideal situation for someone who can exploit other players with a deeper stack).

i dont really like any way that this hand was played but to be honest i cant craft another line i like better.  im not a fan of shoving pre as you have sb who covers you and inexperienced limpers behind you as well. i would bet that their limp range is stronger than your shove range this late in the game and i cant count on all my fingers and toes how many times ive shoved a hand like this, only to have an older man nitroll me with a “weak” hand like [77-TT/AJ]. i dont like raise/calling or raise/folding preflop out of the BB because you miss out on all this potential equity that you can flop just like in this instance.  the only scenario that works well is a complete rarity – where you raise pre get just callers and then bet this flop larger and win it. i doubt thats ever happening.  so checking probably your best bet pre.

flop:

the 6k lead seems okay, but in your spot with the stack size dynamics i might lead stronger in order to make it clearer to your opponents that they dont have fold equity (even if they dont know what that is explicity they still know what it is intuitively). at 6k (3bb) a less experienced player with 14.5 bb might think youll fold for 11bb more and shove more optimally, putting you in a tough spot. but betting 8-10k makes it so they arent able to shove as wide on you. i doubt i ever dont lead here seeing as its impossible to win the pot on the flop here without betting. the only circumstances i could see not leading would be when im sure my opponents are the type to check Jacks they perceive as having weak kickers or not betting unless they have huge hands like overpairs or Jacks-plus-flush-draws. this way we can see turns for free and give up when we miss and face aggression.  

your flop options are really only: bet/call, bet/fold, check/call (never here), check/raise (becomes unavailable here) or check/fold.  and i really dislike all of them. i dont like betting with the intention of folding here but given the action behind you i could see being fine with folding and bemoaning the spot we got stuck in.  it seems pretty clear you have 7 outs the majority of the time here and perhaps even 7 outs while also dodging pairing the board.

without really grinding down a good range of hands your opponents could have with pokerstove i dont know what the “answer” is here but if i had to guess which way or the other: its probably close cEV whether you call or fold but i think with your tournament edge and chip position i'd give it up.

hope this helps