Quite a few "Davids" here - don't know if you mean me, perhaps the others will chip in too.
I presume J3 means Jupiter 3 - I have no experience of this lens, but a guy here:
seems to have found build standards to be highly variable!
If a lens focuses accurately on an LTM body, I personally would not worry whether the focus witness mark is exactly at 12 o'clock. As Leica II and III are virtually identical apart from slow speeds on III only, I am at a loss to suggest why a lens should work on one body but not the other - do both bodies have the correct round Leitz rangefinder cam, and is the cam in good condition in both cases and not worn?