That's actually a great idea. I should have clarified this, I like the J sound better for my band and would actually like to make the P bass sound a bit more Jazz-like
Assuming you are running your jazz with both pickups wide open, then you've got a mid scoop sound going on. If you want the P to sound more like a J I might try to (assuming everything flat) boost the bass and treble on the Rumble a bit, or, roll back both mids a hair.
An eq pedal is a good solution if you are switching between basses during a show, but if you are going show to show, just figure out how to dial in what you want on the amp.
Get in the shed, start with your amp flat, play the jazz, play with the pickups, play with each eq knob on the amp, return to flat (your starting and reference point), get that sound back in your head, then play with the knobs some more. Really take the time to listen, and try to internalize what each knob / button on your amp does, along with the pickups and tone on your bass.
Then switch to the P bass, start your amp flat, get that sound in your head, then play with each knob, return to flat, play with the next knob, return to flat,,, etc.
The same way we can train our ear to hear the difference between a minor or a major chord tone, you can train your ear to hear frequency response, and that can help you know what you like / don't like, and how to get that sound fast. My advice - put in the time to learn what your gear can do and how to manipulate it to get your sound.
