I think the OP is barking up the wrong tree if he's thinking he;ll find a P/T thick neck on a J neck.
Don't ask me how I did it, but in the early '80s I put a 1973 Tele Bass neck on a 1972 Jazz Bass body that was a great combination for my needs at the time.If you like big necks, try a Tele. The only problem is the square neck heel compared to the rounded J style. The scale length is the same as are the other dimensions at the heel. A standard P neck may offer a bit more girth. Hope this helps.

