A normal 3x 3bet would pot commit you no matter what comes on the turn/river, and a minbet looses value if he's on a draw and the turn bricks for him.
I'd just shove and be happy to be called by random Tx, 7x, 9x, and obv flush draws. Obv you're never folding AA as an overpair 99% of the time unless you have a very specific read.

I'd just flat call and see what the turn brings. A lot of turns will force him to slow down even if he is ahead of you, and the hands that you are beating that get it in behind are still like 42%+++ against you.

Just think about why this classic "fish-value-line" is so horribly wrong here - he lets you draw cheaply to a flush or a better straight and destroy his hand.
Without the Ace of Spades, I'd even think about folding against a passive opponent, but here I'd just flat call - any spade is a good card for you, and it'll often shut him down - accoding to the "standard fish logic", AA would always shove here and you're on a flush-draw if you flat, so he may even check the hand down or only bet the river if the turn goes check, check.
As xSCWx said, the hands that you're still ahead against on this flop have a lot of equity against you - and he can also have a lot of two pair type hands on this board.
You're also very deep here with an SPR of 11.75, so you shouldn't be too happy about getting it in with a one-pair hand - but against an aggressive opponent I'd still shove over a normal check/raise if he already check/raised me a few times before, because then it's likely that he's also doing that with Top-Pair or a naked flush- or straight-draw.
Jack