Also, just because the fare basis is J does not necessary mean all sectors can be booked in Y.
There was one example on a Y fare TPE USA on JL. the booking class table says that it is not booked into Y class on AC.
it is certainly possible that J fare on AA only allows I class on CX/KA. it is impossible to generalize, and one has to go back to the fare rule to see what is possible and what is not possible.