If you want something that can do P,Jazz and MM give the G&L L2000 some consideration, couldn't be happier with mine and you will like the chunky neck I reckons
I've done the reverse from jazz to L2000 , couldn't get on with the single coil pickups in the jazz so fitted humbuckers and its a definite keeper now
I think your style and genre of music you play is more aggressive for the single coils of a Jazz bass. You definitely should appeal to those beefy humbuckers more.
I've never played a Jazz bass before, but the clean tone is something I know would fit well in many of the songs I'm playing with my current situation.
What worries me is the neck of the Jazz bass looks pretty thin near the nut. I don't like when the strings are bunched up too close.
That's the one with the sliding pickup. if my memory serves e right they did two other grabbers with diffo pups and then there was the ripper with the oblong head stock
