As played it"s a simple shove for my money.
As I read it there are 3725 chips in the pot and you have 12K behind, any raise commits you and you think he has an overpair. The three bet pre and the flop action means that even if we give him a fairly nitty range of JJ+ and KhQh (which is probably too tight) it is still a good shove as he might fold his AA, KK or QQ here and we have at least 46% equity against his range (almost certainly more in reality) so I am going to CRAI as it is the most profitable long term play.
The inital raise preflop is too large as 400 does the same job and with AJ you want to play a smaller pot, fold to the reraise.