I go for a bright tone - which you don't! I love the Warwick black label strings.
I think you might find that Warwick's Yellow label strings are great for you - they lost their brightness too fast for me but settled into a pretty nice sound that you might dig.
Be careful about the low B's thickness as the string passes the tailpiece. I tried DR Red Devil Extralife strings on my warwick once, and the B didn't fit. DR's coated strings don't all come with a taper B option, but I have some Black Beauties on now which have been great since new years eve. While my next set is going to be Warwick Black Label, I'll continue to use DR Black Beauties sometimes too. But for you - try the Warwick Yellow Labels next. I got mine mailed to Australia from Mike's Chop Shop - he's a decent guy.
Another suggestion is instead of turning the bass knob up on your amp, turn the master volume up!