Didn't say whether you are looking new or second hand.
The Boner Bass (Early 90s Precision Plus) comes to mind. Not expensive for what they are. Just a bit different in the body shape.
.Hot pickups with plenty of output- The Lace Sensor have plenty of output
.Playabilty of a jazz bass- assume you mean- thin neck- this is precision width but shallow
.Alnico/ceramic or single coil pickups (series/parallel switch is preferred but not essential)- series/ parallel with 3 way pickup selector
.Ideally a P/J configuration but again thats preferred not essential- PJ
.Able to handle half step and drop C# tuning- yes
Schaller hardware standard. 22 fret.
Here's a pic from the net of a nice one. I have a natural one but it's not as pretty as this one.
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