Pre: I would not be a fan of flatting JJ here so I like yout fourbet.
Flop: Checking seems OK here, betting small is another option though for sure.
Turn: After villain checks back flop we should have the best hand here very often, betting gets value from smaller PP's and if we check we can potentiall induce bluffs from unimproved Ax type hands so either option is available, I think my preference is the bet though.
River: Pretty gross spot, I can't put villain on much of a range here as I would have expected most hands to be checking back here. Folding seems best as I can't think of a hand where villain is likely to be bluffing with.