Stock p and overwound j is perfect I think to get tonal balance between the two pups, especially in passive mode. I went with a stock American std p pickup and the Duncan sjb-2 , the “Toyota hi lux “ of the pickup world . Overwound, strong low mids and lots of clarity. It is a single coil but if you want him cancelling I would look at dimarzio .
below from Duncan website
Seymour Duncan used that classic jazz tone foundation and added some punch. These pickups are voiced a little lower than a traditional jazz, with a hotter output and fuller low end than the original, giving you boom without too much top end sizzle. The hand ground alnico 5 rod magnets, and custom coil wind deliver a hotter, fatter Jazz Bass® tone with a warm lower midrange growl. The more aggressive attack from this pickup makes it great for all things rock. These pickups are a drop-in replacement for any American Standard Jazz Bass®.