Can you lower the pole pieces on the treble side of you pickup(s)? I play lots of Bob-style stuff with my Telefunken (close enough) and ran into the same thing. I adjusted the pickup on my Esquire and it sounds fine now.
If you can't/won't or it just doesn't suit you, perhaps try a Gator Grip, Stubby, or Tortex pick. They are *similar* to the Adamas, but certainly way less bright.
Is this a 70's bass or a 00's PC...or a Moon Lander? (It's a moon lander) - Tigerstrat