Today I re-wired the bass as planned: passive with stereo out. It's close to a Rickenbacker wiring, VT & VT, except that the pots are 500k, not 330k, and there is a single TRS jack and no pickup selector switch. The P-pickup is wired to the tip and the MM-pickup to the ring of the TRS jack. I may install a switch some day, but until then if I use a mono guitar cable, I only get the P-pickup i.e. it turns in to a P-bass.
I did some measurements, which confirmed that the two pickups are not well matched as supplied. Some typical pickup DC resistance values are listed on the Seymour Duncan website here, where higher resistance generally means more windings and therefore more powerful output. (I know it's not exactly that simple, with varying impedance by frequency, but it's something.)
Fender Jazz: 8.7 kΩ
P-Bass: 10.8 kΩ
SD Quarter Pounder: 11.5 kΩ
Roswell MFR4-N/B (this bass): 4.8 kΩ
Roswell PM-4 (this bass): 15.2 kΩ
That is just nuts, and it's no wonder it caused clipping in the onboard preamp running on a 9V battery. I have the preamp out, and it's all connectors and SMD components, nothing adjustable. The pickups were wired to the balance pot, before going in to the preamp, and that 250k pot is one of those where both pickups are on full in the centre position, and when you deviate from centre, one side stays on full resistance while the other side is shunted to earth. I don't like it - the response was too coarse, as I described above. The 2V / 2T setup gives me much better control over each pickup's volume now.
For a recording test I run a stereo / 2 x mono cable in to the two channels of a Mackie Onyx Producer 2•2 preamp, setting pickup gain separately, in to an Apple iPad 2018,through a powered USB hub and the Apple CCK. In Aum I could set up a mixer channel for each pickup and treat each separately. (The first thing I discovered was that the pickups were out of phase, which was simple to fix, thankfully).
This is the first time I've been able to do separate pickup processing, so I'm just starting to learn how to make it work. I'll probably do a separate post on this later. For example, I tried a compressor plugin on the P and an amp sim plugin on the MM, which sounded OK, but may benefit from some EQ tweaks. With the P signal relatively plain and e.g. a phaser on the MM, the MM volume control on the bass effectively becomes an effect intensity control, so I can fine-tune the effect on the fly. If I use this kind of setup live, monitoring is going to be crucial. It doesn't have to be an iPad, of course: you could run two channels of pedal effects, just beware of potential phase problems. The Line 6 Helix range also supports dual inputs e.g. that's what this guy is doing in his quest for Chris Squire tones.