I think that check-raising flop is better than check-calling with our hand and here is why:
The fact that he is c-betting range for 1/3 pot on this board makes me think that he is not very competent at assessing cbet-sizing on different textures. That, or he just wants to get away with a bluff as cheaply as possible on a board that is good for his range. That being said, against this sizing I believe we should develop a check-raising range on this board. KJ fits the criteria for a check-raise well on KQT.
We should be using hands like AJ, AdTd, KQ, KJ, KT, K9, QJ, QT, JT, JdXd, T9, AdXd, and an array of AdX for our check-raises here. Against this c-bet sizing we can even check-raise hands like K2s or JdXd.

As played I believe that we should check-fold against that turn sizing. We have plenty of hands that can more confidently continue in our range (AX, AdXd, KhXh, QhXh, TdXd etc).

River as played for me is a check-fold but I can see some arguments for seldomly turning our hand into a check-raise bluff.

Very interesting hand Jeff.

Here's my thoughts, relayed against some of yours, too.

Flop:
As mentioned by Kuduku, we'll want to find (at a mix) some hands like this to XR. Our hand has superb qualities; blockers to the nuts/effective nuts, and almost total unblockers to bluffing regions. You skipped flop in your analysis, does that mean you play a pure XC?

Turn:
I don't believe every 2p needs to find a mandatory defend here. Not only is the board heavily in favour for villain, but the board is also double fd'd, meaning we can look to find xc's from other parts of our range, thereby pushing down some of the less attractive 2p's, given their relative hand strength is very similar, with less outs. With that being said, I would have played a pure XC OTT here (solver has it at about a 60/40 XC XF mix).

River:
- Where things gets really interesting -

We've got pure unblockers to bluffs, pure blockers to vbets, and even pure blockers to vbet-calls (good for raising purposes). Long story short, with all of these qualities working together, you shouldn't look to shy away from getting your hands dirty at least some of the time.

As for getting river perfect, I'd like to reference the "a broken clock is right twice a day" analogy. What I mean is that this node is going to be impossible for a human to master, and any successful attempt at such should be down to a high margin of luck and fortune. Moving on, it should be clear that our hand is worth a defend at least some of the time, however, figuring out the specifics is not worth the energy, and perhaps impossible without a solver present every step of the way. Therefore, I'd mix all 3 options, with my only focus on ensuring that I defend more times than not. If that means I XR or XF 15% too much or too little, I move on and try not to lose sleep. Unless I get called, of course. :)