You should try a 5 string Precision. You've mentioned a couple of times how you liked the Fender ergonomics, and Precisions have a very classic growl. I would suggest trying one with the 62 Custom Shop pickups in it. I think most recent standards, specials etc. have them already in them.
In my experience the B string is not so good on P5's. I owned two MIA P5's and while the rest of the strings sounded great, the B's were the worst I've ever played (floppy and "wooly"). Obviously my opinion. But as the OP is looking for "a 5-stringer that would "complement" the JB, with more modern beefier sound and easier growl" a P5 would not be the first thing to come to mind.