Guys, seems I need some advice

I play stoner rock/doom tuned to BEAD. And I use a Rick 4003 (pretty old one from 1984). I own that Rick for about a year and low B was always a problem.
When I install .120 low B it has good attack, but the string is too sloppy - I always have that crappy 'click' sound from my pups.
When I install .130 low B the string tension becomes better but the tone leaves much to be desired - I can definitely hear some detune + the overall tone is near dead.
Overall facts - I did not change/adjust the nut, now it's time to. I know it will provide better tuning, but I'm not sure about the tone improvement. I've also read that tapered strings will work better in my situation, but had never tried them.
Any other advices in setup and strings? Thanks
