Yup, I'd start with the pickups. Wizards are held in hight regard on here, but I've never had any so couldn't say. I've used Seymour Duncan Quarter pounder on a P that was great, and also a GFS set were brilliant - staggering that they're not bigger on this side of the pond.
http://www.guitarfetish.com/GFS-PB-Pro-P-Bass-style-pickups-Sweet-Alnico-Vintage-Tone_p_333.html
I also tried one of their Alnico Super mega ultra hot thingies, and it was everything they said it would be. Superb.