Are you not continuing with a bluff here because while the Jh hits your range it also improves his range so much that firing a bluff isn't worth it? ie. 2h >>> Jh in terms of a turn card to continue a bluff on?

The big issue I see with c/c is that on rivers you don't fill up on he can basically fire his whole range at you if you check. It's going to be a nasty spot.