Preflop I would 3bet to 10 Or 11bb because youre deep with CO and you dont want to let Him setmine profitable. You pot the Flop which seriously narrows down his Ranges. On the turn youre offen up against a Set. Check/fold turn imo.

By overbetting this flop, you make turn really awkward.
I would still propably bet/fold before checking OTT, but i really doubt that you're getting more EV by bombing this with KK into a unknown before using standard sizings.

I can see merit in it only against confirmed stationary-fishes.

BTW, KK-overpair is usually very far from being strong enough to put 240bb into pot with it.

I prefeer 3bet 10bb or more, and cbet 2/3 otf, what you do if utg raise/shove flop?

your reasoning about Kd OTT is bad I think because he can't connect apart from KQs which is a FD+pair but pretty dead vs you OTT. Personally I would go with a smaller sizing OTF, you are deep so I would prefer to pot controll. The board is pretty dry for EP ranges and the CO overcalled which puts him on TT-QQ+/AQs+ type of hands which don't connect with the board(unless he's the crazy guy who flats SCs and small PP 150bb deep, so population=no)

So cbet flop 40% sizing and happy to gii OTF vs CO, unsure vs UTG depends on his open range, but he can have flushes which CO doesn't I think(apart from AQs or AKs).

With this potsize I don't know which hands CO will continue and I think on a Q turn they will fold their JJ/TT so you'll end up valuebetting yourself a lot