But it leaves You with the problem of the imbalance.
If it was my bass i would try to estimate roughly who much the J is too silent, in dB -> level meter of a mixer. With this information i would send the J as a reference to a custom pickup maker and tell him how much louder it needs to be. And i would of course order large magnets.
In my Witch shown above i could successfully avoid this: i replaced the DP122 by the original split coil, 10.3 k with Vester Logo. It is a bit noisier and sounds a bit less fat tha the DP122, but its tone is pretty much ok. The J - a DiMarzio DP148 - has still a bit less output than i would prefer. But it is possible to obtain a balance between the two PUs without turning the P ridicoulously down into the cavity while even keeping a reasonable distance to strings in the J position. Nice.
And the bass is a little bit closer to its original optics. Nice, too.
BTW: the DP122 is built similarly to a P90 guitar pickup: to magnets attaching the pole screws below the bobbin and like al P-split coils relatively flat and wide bobbins. Has someone tried to swap the magnets against Alnicos or just to remove one magnet in each of the pairs?