Re: Fretless P Bass
Now, on to the pickup question.
IMO, compared to some of the OP's extensive/expensive instrument collection, a Fender MIM Standard bass guitar might be thought to lack character. The obvious solution is to let any replacement pickup and/or electronics define the tone. In short, that means going active.
My ownership experience with active fretless basses is as follows.
1) 1978/9 Fender Precision. Ash, maple. 1 x EMG-P pickup, standard unpowered controls.
2) Yamaha RBX-200F. Asian Alder, maple, rosewood, cissy position marker lines, Gotoh 201B bridge. 1 x SD Basslines Lightnin' Rods P Bass pickup. SD volume pot, EMG TBC active EQ.
The Fender is strung with Rotosound BS66 43-110 (Billy Sheehan) roundwounds. It sounds huge. There can be an unpleasant "glassiness" to the sound. Possibly, a little too much of the string wrap noise coming across. After twenty one years, I have grown a little jaded with this sound but, having used it on numerous recordings, it has to remain available.
The Yamaha is strung with D'Addario 40-95 roundwounds. Unexpectedly, this bargain basement instrument sounds wonderful. Even with a single pickup, the bass manages to combine the woodiness of a double bass with some of the "neeoinng" of a fretless Jazz Bass.
I have also experimented with SD/Basslines Pro Active and the older SD Active EQ "switch" series pickups in fretless instruments but was never entirely content with the results. These models seem to sound better with fretted basses.
My favourite fretless bass guitar is my Musicman Stingray 2EQ. Obviously, on that, only the EQ is actually active.
For a passive bass guitar pickup that sounds as if it could be active, try the Bartolini 8S replacement for Precision.