3-bet pre is okay. Check-call flop or bet 65% PSB OTF. Check-raising is the worst of the three options. Overreps your hand and isolates yourself against a stronger range. Once you get called, you might be drawing pretty thin and maybe only spades are your only outs. Also, you get put into a really crappy spot if you get shoved on. You'd probably have to fold, unless Villain is the type to stack off with TPTK/TPGK300bb deep, which is super unlikely.
I prefer check-call. I think people misplay TP + FD/ pair + FD type of hands. Right now our hand has SDV. The fact that we have the NFD does not change that or make our hand have anymore relative strength than it does if we did not.
We do not want to get raised off our hand and blown off our equity. Or have to commit with this type of hand for 300bb. Checking also opens up their bluffing range. Also, there are very few bad cards for you in the deck, so there's not much of a reason to start shoving in money to "protect" your hand. Fwiw we bet only for value or as a bluff. When you raise here, you must have many more WORSE hand combinations in Villain's range that are going to call a bet in order for this to be a value bet. But I don't think there are many worse hands that are calling. Essentially here you just turned your hand into a bluff, but no hand better than yours is folding (flushes, Q10s that got frisky pre, 1010, QQ, 66). When you start raising on any type of board, especially monotone boards, you're isolating yourself against a much stronger range.
As played, shoving is the only option. Not great, but we have less than a 50% PSB left. I expect to lose here a lot, very rarely be good, and sometimes suck out on the river if he ends up calling, which is going to be pretty often.