A Sandberg VM4 would be the bass I would buy to accomplish everything on your list. It can handle the Fender P perfectly using the front pickups, Its got a double bucker stingray style pickup and emulates a stingray very well, and just about all the other sounds on your list. It is BOTH active and Passive (pull the volume up and its passive, push down and its active). Just my 2 cents. I'm a Spector NS2 guy but purchased a VM4 and have found it to be the most versatile bass I've used in 30 years. I find myself reaching for it for every style of music.
