I customized a Musicmaster Bass years ago that turned out quite well.
I replaced the stock bridge with a Leo Quan Badass 1 (routed 1/8" into the body). I used two DiMarzio Model G pickups [I don't think the Model G is still available so I would try the Schaller Bass Humbucker or Bartolini 1C pickups]. I cut one pickup in just in front of the bridge and replaced the original pickup without changing location. Both pickups have series/parallel switches - neck pickup is a mini-toggle, bridge pickup is (volume control) push-pull pot. There is a mini-toggle pickup selector and the tone control is push-pull pot for phase reversal.
The tone ranges from classic Fender P-Bass all the way through to tones that are "Alembic-esque" in nature.
I loaned this bass to a friend of mine to get his opinion of the sound and he kept it and recorded with it for 23 years! It finally came back to me a few years ago.