Should I replace pickups in MIM PJ

So I recently acquired a very nice 2002 Fender Precision Special Deluxe (Passive P/J) on the TB classifieds. I love the way this bass plays. But I keep hearing about how low quality the MIM pickups are and that practically anything is better.

I have it strung with GHS pressurewounds with the neck P solo'd nearly 100% of the time with the tone rolled almost all the way-all the way off.



This is a cover my band recorded to give you an idea of what this bass will be used for/sounds like right now (first time I ever really recorded anything myself, but I think it turned out okay). I recorded the bass in Garageband through Tech 21 BDDI. I personally think the bass sounds pretty good. But I am used to playing cheap crap and I thought my old bass was fine until I got this and now the action feels SO high on the other bass (changed strings on both basses/setup when I got this one) so who knows maybe I'm tone deaf and these sound like crap. It definitely don't sound as good live IMO. They are boomy to the point of kind of muddy, but again not terrible.

I've been playing bass for awhile now, but I am new to this whole "new gear" thing and don't have much experience owning/playing a lot of different instruments. Meaning: I don't really know what I want...

I think what I am looking for would be classified as "vintage" or that "classic" p bass sound. I definitely don't think I want a super modern hi fi sound for this type of stuff. I like the thump and boom, but I could use more clarity and definition of the notes. In a lot of the original stuff we do, I do some bass fills/solo-y stuff to compliment our less "technical" lead guitarist.

The J pup, as of now, is just there, but I can see myself using it if I start playing metal again or for more upbeat songs. Really not that important to me; kind of wish I would have gotten a regular P (just for looks), but the J isn't really in the way or anything and I like having it in case I need it I guess.

I was looking at the SD SPB-1 (Vintage) and through my research seen it recommended with the STK-J2 (Hot Stack). Does anyone have any feedback on this setup? I'm not entirely sure why I need the "hot" j pickup and wonder if I would be better off with the STK-J1 (Classic Stack).

Should I do this or just buy a set that comes with both pickups (like the Dimarzios)?

Also I hear Fender currently use CTS pots and was wondering if this bass has those as well. Either way I'm probably not going to mess with the pots/jack unless persuaded otherwise. Through research I have found varying schools of thought on the subject, but leaving them alone seems easiest for a newbie at wiring electronics. Even though it really doesn't seem like it could be that hard.

OR

Of course there is the option of leaving it the hell alone and being happy with it as is. I was planning on changing the anodized gold pickguard out and figured while I had that out I might as well replace those "cheap crap" MIM pups....

Sorry for the long post, but I always like to be clear and tell the whole story to get the best possible answers. I've been up all night researching this topic before posting so I would have as much information as possible before I posted.