I guess I should re define "hot rod" pick ups. Pour choice of a term.
I guess what I recommend is using "good" pick ups.
Replacing the stock Pick ups on lower end instruments can make a world of difference. not just for tone , but in way less noise and shielding issues. And sometimes a well played older instruments need an upgrade too, must be the magnets die of old age.
There are so many different P bass's made all over the world, you cannot trust that any 2 would sound the same.
Op- have you tried using just the raw bass track without all the fancy gimmicks ??
Somehow I can't help cringing when I read your using guitar rig to enhance the bass. I guess I'm a purist and other than compression and a touch of EQ would never dream of processing bass. I'm the same with guitar tone too. Guitar-Cable- Tube Amp. But then each type of music requires a different approach I guess.