it feels like he has bit more missed draws than made hands here, taking into account we block the king.

shoving aims only for making him lay down 7J, which he woun't always go for and some naked K***

check decide is fine, imo. as he mostly not turning into bluff weak made hands (some J7, random 73 or so) and have too little behind to bluff shove the river w\ FE.

kind of close between shove and c/c for me.

I think c/c is better, as said only hands he might fold that beat you are J7/K7 and I can see him calling with those a decent %. x/decide would probably be a call as he probably isn't valuebetting K7 here and can't have much better.

I think that shove and c/c are going to show near the same expectation in this spot.  I would probably go ahead and bet the river to try and fold out AK, and small two pair type of hands.  Your range is pretty strong here so think that we can go ahead and bluff the river with this hand.  In SSPLO I find so many players fold to river bets, and call turns/flops too light. 

I actually think that on the turn we bet too big given the off suit brick.  I would actually bet a little smaller here.  I don't hate life if I get raised because I do not see a lot of hands that improve on this card and we actually allow villain to semi bluff with the Kxx combos that we have crushed.  When you bet so big I think that it handcuffs villain to calling with worse or raising with better.  I would like the bigger bet size on a second suit card or one that completes one of the many straight draws.  But on a dry semi connected board we can bet small still get the small amount of folds and I think induce some spazz shove from KQTx, 789T, 89TJ.  Depending on his side cards we are 50% against two pair hands but really only see KJ or J7, and I think that KJ would just raise flop.

I would be b/c calling a lot of my KK, JJ hands and b/f these missed draws, using my Kings up hands for bluff catching and maybe J7 depending on villains river aggression.  I think that this should be a good mix considering that the board is semi connected and we will not have a lot of draws in this spot (they will mostly be so strong that we have played them like sets the whole time).

We're playing the river for one bet, so we bet our best and worst. We check hands in between, check-calling with the best of them and check-folding the rest.

Our range should be pretty strong after raising UTG and betting twice, so we should be able to valuebet often and bluff the corresponding amount. However, if you bluff a hand as strong as this, then there might not be much showdown value left in your checking range (since J7, J3, 32 etc type bluffcatchers are rare when we raise UTG and bet flop + turn). Also, we should have plenty worse hands that can be used as bluffs.

There's also pot odds and bluffing frequency. Villain is getting around 2.5 : 1 when you shove, so ~72% of your bets should be hands that do well against his calling range. Betting this hand could mean we are bluffing too much.

So I think this is a check for me, hoping to show down for free and win vs Villain's busted draws that give up. If he bets, it seems like another close decision between calling and folding. It depends on how our checking range is built, and I think a little analysis is needed to make an informed decision about that. 

At any rate, check-decide seems like the play here.