While different pickups can help, I agree with those recommending a series/parallel switch first. The parts are cheap, and any good tech should be able to install it easily. Wiring J pickups in series doesn't replicate P-bass tone, but the additional low mids fatness give it a P-like presence in the mix, sort of like the Lace Man O' War pickups I recommended earlier. It's a useful tone, as I learned with my 2003 Fender, which has the S-1 switch.
I wouldn't recommend wiring the pickups in series exclusively, because then you lose the ability to use different pickup blends.