This may be a little out there, but you can pretty much achieve your goals with an L-2000 with the K-mod switch to allow use of single outer coils. In single coil mode it's pretty close to a jazz bass with a p body and wider neck (Tribute L-2000 has 1.75" nut width) and no pickguard. Here's what you get extra: bass and treble cut controls plus all the various humbucking options in series and parallel—a heap of extra interesting sounds. Here's what you don't get: separate volumes to blend the two pickups (selector switch instead, neck, bridge, both) and MFD pickup design rather than the standard alnico magnet jazz pickups. The latter might not be much of a loss, really. The K-mod isn't very hard to do if you have a modicum of soldering experience.