I'll start with a disclaimer here that I've never played above $2/$4 live and this is way out of my level, so take everything I say with a grain of salt.
Anyway, my analysis would be:
Preflop: it's fine calling here, since you have a 350bb effective stack against the villain, the 3bet was only a raise to 9bb and there could be plenty of marginal hands in his 3betting range (given that this is CO vs MP), such as JTs or 22.
Flop: I am fine with check-calling here too, since the villain is going to Cbet the flop and then give up a lot on these kind of boards with hands that completely missed, although I wouldn't actually fault you for folding here, given that it's very hard for you to continue with this hand the times when the villain barrels (and the villain could easily be barreling a semi-bluff on this board texture).
Turn: Checking is the only thing that makes sense here. You are typically going to be checking this turn with 100% of your range and I don't think there's any real reason to deviate from that plan.
River: I like the overbet because it makes it unprofitable for the villain to call here without a diamond, and it's also very credible for you to have the Ad or a straight flush, given the line that you took. Once you get raised, I think it's fair to discount everything from the villain's range except Ad, a straight flush and a complete bluff. I think it's safe to assume that the villain will flat-call you with any diamond below Ad, which makes his raising range very polarised.
But here it gets interesting: you know you can't flat-call, but you're contemplating going for the 3bet to get the villain to fold all his bluffs, as well as potentially folding Ad. I personally think that it's a bit optimistic to expect the villain to fold Ad, and let's look at it from the villain's perspective: you shove 8.5k, meaning he's calling 6k more to win a pot of 18k, giving him 2:1 odds on a call. He only needs to be right 33% of the time to make this call, and I think that he'll think that there's about a 50/50 chance that you're bluffing here. It's admittedly very hard for you to be bluffing in this spot, but then it's also very hard for you to have a straight flush here, given that there are only 2 combos of SF's, with 56dd being difficult for you to have, and you chose to check-call the flop, rather than check-raise the flop, which reduces the possibility you have JTdd. I think that if you check-raised the flop, the SF would be a bit more credible (I'm not saying you can't have JTdd when you check-call the flop, just that I think that it's less likely you'd check-call it rather than check-raise it), but as played, I think that the villain is going to be calling any raise with the Ad.
So by 3betting here, I believe that you're only folding out his bluffs and you're getting called by any Ad or SF combo. The question now is: how much would you 3bet to? Shove or small raise? Given that he raised to 2.5k and your maximum river raise sizing is effectively 8.5k here, there's not too many options about raise sizing. And what does it look like when you raise here anyway? Let's say you have Ad. Are you really raising the river with Ad? What worse hands do you expect are going to call your raise with Ad? We already concluded that the villain never has a diamond below Ad here, so you'd be far better off flat-calling with Ad. That means that when you raise, you're only representing either a SF or a bluff. But when you raise small (like 4k for example), is that really representative of a SF? Wouldn't a SF want to shove the river in the hopes of getting called by Ad? So the only options seem to be either shove or fold, with shove representing either a SF or a bluff whilst getting called by Ad and SF and folding out bluffs.
So the question is then about
pot odds: when you shove 8.5k (7.2k more) to win the 5k in the pot, you need the villain to fold at least 60% of the time to make it profitable. Do you expect that the villain is going to show bluffs here at least 60% of the time whilst showing Ad and SF combos less than 40% of the time? It's close, given the history you have with him and his willingness to play back at you, but honestly, I think that the probability that he's bluffing here is below 60% and thus it's better for you to just fold the river.