Disclaimer: I have no direct personal knowledge of this subject.
That said, from reading what everyone has written both here and elsewhere, and from the public history of the two services involved, and from personal experience with a military bureaucracy (USMC), I would suspect that the "joint JAP system" was the RAF system with the pages re-labelled.
After all, why make both services learn new procedures, etc when the larger "partner" has already been operating the only remaining type to be used?
Keeping the RAF way of dealing with the GR.7/9s would save a lot of money* over creating a whole new set of procedures and making both sets learn the new system.
I also suspect that while the SHARs were in service in JFH, that the RN types were dealing with them the way they had always done... and training any RAF cross-overs in the RN way.
*the prime goal of the Treasury-controlled MOD in these times.
PS: Engines confirmed this while I was typing it.