About preflop decision: on the small sample I had, he had been pretty tight pre.

I gotta admit i'm really clueless about what to do on the turn here. In the end, I thought I'd split with Ax enough times to make this a call. Thoughts?

well this is an hand that we are happy to shove preflop (it will not have caused all this postflop problems). I don't mind either calling or raising on the flop but if you raise then checking the turn seem weak so I suggest you to continue leading,at least b/f, as played villain's river bet is strong and as you said in the introduction he plays tight. I think we're beat, fold and look forward to the next hand.

I'm not sure here but I'll give it a shot as it means I'll come back to see what other people say...
You can probably still jam pre, although I still flat weaker aces >20bb myself
Flop - I think you can raise a little bigger as villain likely has a piece of the board.
Turn - Now I'm treading carefully. I don't think I can fold here though. I do like the call as if you jam you're pretty much only getting called by a king or straight.
River - Call imo. Not loving life here but I think you're right about splitting with aces.

I'm really stumped here, maybe someone else can have a better go

I think a lot of the problems people are having in these spots is from there disregards of the future PSR after the flop raise.

As played, you have 320 left on the turn in a 280 pot, which sucks, as every bet commits you when he isn't commited yet and while any bet from him commits him, he has the chance to check back that you don't have.

First of all, don't jam pre if he was tight so far.
Then, I think a call down here on most boards is perfect.
If you want to raise the flop (and I don't know if that's perfect, you'd have to empirically solve this I guess), make it 140. Reallistically, a fold from villian isn't that bad for us with most hands, but a call from weaker hands tends to be a much bigger mistake here as now there's 360 in the pot and we have 280 left, so the turn becomes a shove more easily (and he will be more inclined to call that with hands that you still beat). I don't think the K should scare you too much there.
Another thing to consider is, if you raise to 140 and get to the turn, if you check he reallistically doesn't have the option to bet smaller than AI anymore, which really plays to our advantage too.