So here's the thing about mid scoop when discussing two-pickup instruments: It's not as simple as "X frequency is scooped so boost it" because each string has its own scoop frequency.
So the solution is to be a combination of a few factors-
-how you play, including and especially a) your right hand placement and b) what fret range on what strings you are choosing
- how you eq your instrument based on the previous point specifically
- circling back to how you play the instrument in terms of the previous two points
in other words, you have to let the bass inform the grammar of the musical language you speak through it, and not the other way around.
In a more general sense, it is a pretty classic educational benchmark for bassists to realize that 'if it sounds good alone, but bad in a mix, then it actually just sounds bad.' Or to translate it into something more fun, and less disappointing, We have to know in which moments the song and arrangement would sound great with bedroom tone, and which don't. If we do things right, The idealized version can often be such that we change the solo based tone such that when it's in the mix, it gives the illusion of having bedroom tone, when in reality the solo tone would sound much harsher or honkier or whatever by itself.
Now more practically, and based on my own experience, For those non-exposed moments when the base really has to support them mix rather than be featured, as a rule of thumb I tend to find that I need to favor one pick up over the other… For my purposes, I usually find that to be the P but for many others, it will be the J. In light of what I said earlier, once you have dialed in your physical and tonal approach to the instrument itself, a subtle boost to the mids in whatever range helps .. well.. helps. For some people/instrument combos, they need to add in the upper mid attack.. for others, it's the normally nasally middle-upper-mids that somehow sound amazing in a mix.. and for others they just need the and punch of the lower meds enhanced a bit. But again, none of these are because that frequency alone is what is scooped, but rather that the combination of our play style and the instruments quirks result in an average need for xyz.. again, each string will have its own distinct comb filtering, So, unless you only play on one string, it's not as simple as picking out whatever frequency gets scooped.
and as others, joked, the sound of the guitars does matter… if they are very middy and rooty, then something has to give between your place style, your bassline, and the instrument itself. I had a love-hate relationship with PJ instruments.. Part of that was that frankly, I just don't think fender PJ's are very good, whereas the cheapest Ibanez has an amazing PJ sound.. But the other part of the equation that took me a long time to figure out was that I really enjoyed playing PJ in funk and jazz groups, where keyboard was the main harmony, and luckily some very good guitarists Understood how to be a rhythm instrument AND UNDERSTOOD HOW TO MAKE THEIR TONE WORSE TO MAKE THEIR TONE BETTER, or else with no guitarist at all… It took me a while to realize that every time I was in a guitar heavy group I liked my tone a lot less on a PJ
I realize that a lot of that was a non-answer, but hopefully some of those reflections can help you to inform your approach, because I don't think there's a super easy answer other than 'play a different bass,' and I don't like that answer at all