Interesting that no one has mentioned the 'sweet spot' theory.
IME, and I've had a few P/J basses and far too many Precisions, having a P/J setup pushes the split-P pickup closer to the neck to make room for the J-pickup.
Whether or not there's a sweet spot, that move has to change the sound of the solo'd split-P as opposed to an equivalent Precision layout.
Sounds like a very odd (and pointless) arrangement. IME you either put the whole band through the PA or you have backline and put vox only through the PA.
Your arrangement appears designed to give you the worst of all solutions.
Has your 'band leader' explained his reasoning? And will he listen to reason?
Is there a prize we can award for the most dispiriting, negative, unpleasant topic of the month?
Not the OP, not the subject matter. But the blend of arrogance, condescension, generalisation and pigeon-holing that has been attracted.