First compare it, same amp, same cable, no effects to a "know good" guitar. Make sure it is the guitar. You don't want to change the pickups and find you have a bad cable! You want to eliminate the cheap and easy problems before you go shopping.
6mm seems a bit much...I just had my first experience with "stratitis": pickup too close, horrible dull sound no sustain, impossible to intone especially 6th string, pulled pickups back to about 4 mm (open string, much less when I fret up high) and viola, a clear and proper sound with the ability to set intonation. So try closer and pull back when you get horrible dull mush.
After that, with a Strat, it is a matter of loosening strings, removing pick guard and getting into the harness, the "electronics" (three pots and switch) and the pickups themselves. No volume until 9 or 10 might be changed by taper of pot; a linear taper takes a long time to get to that useful range, the audio sweeps up there faster.
And then you might try things like snipping some wires and wiring a pickup (and bridge ground) directly to a jack, no pots, no switches. And find out what a PU does by itself.