Personally I would stay away from the PJ's since I don't care for the tone they have. But any of the JJ's, heck yes! There is no such thing as a bad Sadowsky. 
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Indeed!
I'm genuinely curious about how close you can take your hc pickups toward that growly, slappy upright sound that seems to work well on old-school country, emulating upright hitting on downbeats. No doubt the hc will do warm and smooth, but given the OP's query, I thought he might also be looking for a broader range of attitude...
There are a million stories in the naked city...
By blending both pickups at 50%, VTC off and treble all the way up, one can approximate the sound you describe, but it won't do the typical full-on jazz growl (which is no problem at all really).
Warm and smooth....boy oh boy. I tell ya, when I first gigged this bass, she sounded so warm I had to remove a layer of clothing... It's a GREAT bass. The 'B' string is superb.