WOW. Just wow. I was positively shocked at reading this. I spent a lot of time on how to respond effectively and politely. I don't think I did a very good job with what I came up with, but regardless, here goes...
I played bass for 21 years, 14 with a road band, struggling with record deals and all the crap that goes with it.
After that, I entered the sound business and became a pro sound guy, mixing for several region groups and assembling, tech-ing, maintaining, and deploying the largest PA in the state (which, considering the state, isn't saying a whole lot, but we did with with several hundred national acts over my 21 years with this company). I am still the FOH guy for the MS Symphony Orchestra, and for two years, I've been playing bass again, pretty much full-time, while working part-time at that PA company doing repairs and up-keep.
All this to just list my references and resume before I make my response.
As a soundguy....I have never....EVER...felt the need to ask a bassist to adjust the balance between the pickups on his instrument. EVER. I've run into other issues (buzzing, bad cords, sloppy technique, etc), some things I can address, some things I can't. But one mantra I followed my entire career was to never tell a player how to set his instrument. I would offer solutions to problems (the aforementioned hums and buzzes), but I left their sound and tone alone, UNLESS ASKED, which did happen from time to time. What I was getting wasn't always pleasant, but I worked with it as best I could. I don't know where I stand in terms of being a good or bad soundguy, but bands and musicians loved me for the reasons I stated. As for basses, I understand that some settings will scoop the tone somewhat. I never ran into a bass sound I couldn't do something with, unless the stage volume was over-bearing. Again, I wasn't going to say anything to the player unless asked.
As a bassist...I've never...EVER had a soundguy tell me that the balance of the pickups on my Jazz bass needed adjusting because of problems with the tone. I set them both at 100% for the Jazz bass sound. The phase issues you mention aren't phase issues. Phase issues are a result of problems with time and frequency. In the case of a bass, you'd have to have the signal from one pickup slightly (in milliseconds) delayed or behind the other, causing a null (cancellation) when the two signals are combined. I can't see this happening with the bass. In the case of Jazz basses, I think (guitar techs, tell me if this is incorrect and what the real answer is) the two pickups are wired out of POLARITY (BIG difference between phase and polarity. It will expand your PA knowledge greatly when you learn the difference). This is why each pickup might pick up hum separately, but when combined, they (mostly) cancel the noise. Other pickup arrangements offer dual-coil pickups with switches to make the coils parallel or in series. You might be dealing with with some of this with the other players basses.
You may have other issues as well, but I'm trying to wrap this up quickly as I have other tasks to get to tonight. But I felt this really needed addressing. You really need to look elsewhere for the problems you are experiencing. Or perhaps a bass just has problems that need to be repaired.
Good luck....