SchKumBACK

secondhander, your line would be great if we block the nut flush having the Ah, without it the majority of his flushes will be the nut flush, and it all will depend how thin he will value bet/fold the river. It could very well still be good depending on what kind of player we are facing, but definitely in my opinion if we had the Ah checking with the intention of winning some % of the time when checked behind, and turning our hand into  a bluff when he bets would be very good.

And yeah I wouldn't care one thing about people saying our hand would be too strong to turn into a bluff, blah blah balance, if at any point we can change a xF into a xR for higher EV we should do it, period. Remember you are playing poker for profit, profit comes from taking the highest EV plays in every spot, lets just stick to that. Same goes with the thinking of your range being capped therefor you should bluff catch, it is all a bunch of bullshit. You should bluff catch when your opponent bluffs often enough so you have a +EV call, it is true that certain players will bluff more when your range is capped, but that doesn't mean you should call because your range is capped, it means you should call because your opponent bluffs enough, the reason for him bluffing enough shouldn't even matter to you any way.

We can't talk about his range if there is no information provided whatsoever. Above analysis is all guesswork, you can't discount anything in this situation to a comfortable confidence level really.

Yes it make sense for villain to raise sets/FD's on the flop, it also makes sense for him not to do this. Villain could easily want to get the BB in the pot, since we know nothing about villain we can't discount sets whatsoever.

He can have boats 99, he can have quads 66, he can have trips 67s/A6s, he can have 2pair KT, he can have straights 78s.

So he can have plenty of value combos, your line looks reasonably strong with barreling this turn. And people do not bluff this call call bet lines nearly as often as you think. 

But really with no information no real quality advice can be given.

Keep in mind that the hands you want him to bluff with are:

Axcc, QTcc, TJcc   which also all could have showdown value in villain's eyes.

Given that we need to be good here about 29% of the time, I am fairly confident that you are never good here often enough, specially with no information.

Having his BIP %, AF, and RB % would help a lot in this spot.

Your deviating a standard bet/folding strategy based on a low FCB % and a relatively high cold calling %, while after 1.3k hands these numbers aren't as definite that you should base your whole line on this. 

Also you are missing a lot of information you need to have to make xCalling better than a bet/folding line. 

A few pointers:

A low FCB% means nothing more than what it means how often someone folded to a CB so far, and your sample size is pretty low on this.

You need to know how he plays the turn, Bet in position % (BIP).

Next step you need to know how he will continue if he bluffs turn a lot, will he follow through on river?

Combination of AF/WWSF/RB% would help there.

As played definately fold the River, +EV calling here is so extremely situational and you really do not have the proof for the situation that is needed to do so (you even have very very little information, you based everything on stats that don't have a big enough sample size, and you seem to not even consider follow up information needed to proof your strategy).