You could try an overwound Lindy Fralin Split-Jazz, which is a series wired split coil in the J shell. The stock wind sounds like a beefy vintage voiced J pickup, but an overwind should move it closer to P-bass territory. I'm sure Lindy would know how to best emulate a P-bass tone within that format.
"After awhile, it's hard to separate cars, women and rock 'n' roll in your head." Brian Johnson, Autoweek, July 9, 2012.