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I have that exact bass. I removed the pickguard and added a noiseless J-Bass. Now it's a great desert island instrument. Congratulations!
Adding a noiseless J pickup (70's position) to a P bass with VVT configuration. Did it to both of my P-Basses using Aguilar HC-J pickups.
I don't mean to be snide; but this looks like the second Fender StingRay attempt - following the discontinued Dimension Bass. Let's see...
A decent PJ (preferably noiseless) should get you far enough.