The Perfect Tone

Now this is just me, but I think a really cool bass tone that I want to have is the bass of Matt Sharp of the Rentals and formerly Weezer.

I'd like to get the bass tone from Weezer's first album because it's me. Matt plays a frankenstein bass consisting of a Warmoth Telecaster Bass-style neck put on a 70's Jazz Bass body and Scheckter pickups. For the recording he ran that bass through an Ampeg B-15 head and an Ampeg SVT 8x10 cab.

If anyone knows what I'm talking about, any suggestions on how I can turn my Fender P-Bass, Highway 1 Jazz Bass, or Modulus BassStar into getting that kind of tone?