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How often has Villain shown down? I.E., what's the apparent likelihood of pushing him off an A or small pair?

It's possible, though somewhat unlikely, that you have enough equity to raise for value on the flop even without any fold equity (but that would assume we're planning to show down UI a lot). I prefer to just check/call vs this sort of guy -- we've got a couple overs and a couple backdoor draws and Villain will almost certainly keep firing. We can reevaluate as we go.

The way the turn and river came down, I like a check/call, check/call, bet/call line. The A is somewhat likely to have hit him, and it's a good bluffing card if not. Our flush will often be good so we don't want the river checking through, and this guy seems LAGro enough to raise a worse hand on the river.

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Well, the sample size is pretty small, but he didn't show down that often. As much because he folded people out as he folded himself. He won 2 out of the 5 showdowns. I don't think I would have pushed him off an ace or small pair, but if not ahead, he of course likely has lots of outs. From what I saw, I might have been able to show this down UI, but I see what you mean about a c/c line vs this type.

If I would have c/c the flop, I would have c/c the turn and b/c the river. The flop decision kind of dictated how the rest of the hand would be played given the turn and river cards.