4 people in the pot? I would totally shove with that scary flop. Easy decision.
Chances are you have the best hand on the flop, and you want to try to chase away people drawing to the flush (and maybe a straight). You also want to punish chasers by giving them improper odds
to calls their Ad/face or J/Q (open-ended) or A/T or whatever.
As it turned out, A/A would have called your shove, and you'd have have close to a 2/1 advantage over the guy. Yummy!
When the J came on the turn I'd be done with the hand.