Somewhere in the Classifieds here there is a very nice, well priced Billy Cox Signature Freedom Bass by Cort--it is PJJ, not JPJ, but may give you whatever it is you want.
Its the other bass Fender should have made. Lol. Warmouth could do the body with routes. Id wire for 3 little toggle switches for ind pup on/off. So you can do any of the possible 7 combos. Hum free J pups of choice for the J's so no issues with hum etc. P pup of choice. Prob nuther switch for active/passive. 3 band preamp with sweepable mids. And std pasive tone for when in passive mode. J neck for slimmer easier playing. Would you want the P to be traditional or reverse? The latter can give better tone balance for some, little better articulation for lows and little warmer highs. What color would yoiu do the body in? Lol. Could be real nice custom warmouth jpj bass for not too much money.