Standard PJ's will always be a compromise. As has already been said, J's are single coil and hum while P's are a hum-cancelling split pair. Adding a switch to reverse one coil on the P can 'un-hum-cancel' it to so it can then sort of hum-cancel with a J, but you then have out of phase issues with the reversed P coil etc. Half of the P would be in phase with the J while the other half is OOP, so two strings would sound thin and nasally... which is probably worse than the hum. There are some other things you could do, but you still lose all the good things about a P.
I'd say go with with a standard PJ wiring or, at most, add a series/parallel switch on the P. It won't make it hum-cancel with the J, or put it out of phase etc, but it does give it a different sound while still keeping it a hum-cancelling P. Then, keep your eye out for a cheap DiMarzio Ultra Jazz hum-cancelling bridge pup and stick that in if you get the chance.