Some of these sound over complicated. I use a Blackstar headphone amp. Just plug and go. It does have a rhythm machine built in so you can practice playing in time.
You should check them out early Jack Casady’s made by them, all Epi semis. Martin Taylor had a signature model made by them and he’s pretty discerning.
Peerless have made great guitars and basses for other companies, Epiphone, Gretchen etc. They have made some great basses under their own name so show us what you have - Retromatic, Smoke, Bassmaster Player, anything else?,
I wonder if you really need to change those pickups. I assume it’s active with all those controls and if you can’t dial up the sound, why not get a preamp system which offers different sound patterns and amp simulators. I suspect what you are looking for is a particular artist’s sound when using a JayDee. It may be the amp/speaker combination that you’re really hearing.