What jazz pup to complement a Precision V-Mod pup?

Don't over think. I would also most definitely go with a matching V-Mod Jazz pickup. I love the V-Mod split pickups on my American Professional Precision.

 

Metal and Rock Guitar Pickup | The Aluma P by Lace. Hi Definition Drop in P bass pickup made special for low noise and huge output, gain and sound. for 4, 5, and 6 string basses.

with this option you could try out various positions. Also, if you don't want to route and don't mind seeing an exposed lead you can go back to stock at anytime.

 

you likely want a hum-canceling J pickup or you'll get noise, and if so you definitely want a "split-coil" design rather than a stack so it doesn't sound so weak.

the question then becomes finding one that lines up with that wide-spaced bass.

i'm sure nordstrand can do one, maybe the new duncan apollo 5-string J?

 

These are the dimensions of the wider 5 string Apollos:
Neck
Bridge