Placing a pickup too close to the bridge will cause it to sound thin and weak. Also, these Barts are 4-conductor, right? I recall you mentioning that you split them out to single coil... Do you ever note better low end response when in single coil mode? If so, your wiring may be faulty, in that the coils may be out of phase. I have a friend in college who had an MM pickup added to his P-bass in the bridge location, but because he didn't want to mod the pickguard, the MM pickup ended up being too close to the bridge and sounding like crap (it was also wired out of phase, which made it sound thin and midrange-y, but even after correcting that issue, it was still thin and weak sounding). His only solution now is to either fill the hole, re-route and refinish, or to replace the body.
1M tone pot should have a HUGE sweep through it's range. There should be a marked difference from one end to the other, if it's properly wired, ad the cap value is correct. I'd double-check the tone cap value, and that it's wired up right.
All factors of your electronics will affect your tone/sound. Your issue could be related to bad components, bad solder joints (less likely, but could happen), incorrect wiring (series/parallel/phase on pickups), etc.