Chinese Custom Shop?! Anyway, the EB-3 and the EB-0 have a muddy sound, especially their neck pickup, perfect for '60s music. I think you should try one before buying it: you may not appreciate this bass. It's totally different from a P-Bass or a J-Bass.
-Guitar: Squier VM Mustang, Squier CV '50 Duo Sonic;
-Amplifier: Hughes&Kettner Blue Edition 60;
-FXs: Dunlop Cry Baby GCB-95 Wah, Boss BD-2 Blues Drive, Proco RAT, Danelectro Cool Cat Tremolo, EH Small Clone, MUZA FD900, Bespeco Volume pedal.
According to what I heard it might be good for some fuzz tones and can do it better than traditinal P and J basses. To my ears all Epi pickups are somehow muddy, maybe adjusting the height will help, but I think it is more about how they were built - the gap between Epis and Gibbys has to be noticeable, if you know what I mean.
The DiMarzio Model One is a common mod, I think it sounds good but don't have personal experience, except I knew someone with one of those basses and I didn't like the stock sound.
The Model One is a good p'up where it is loud, boomy, and no mud. You can put it in straight or wire it up for series/parallel (single coil even, but it sounds very much like parallel). Of course, I have one in a Bronco so your bass, opinions and experience will vary.