Good list but I'd like to make a couple of suggestions.
Didn't Larry Graham the father of Pop and Slap play a Jazz? I think he deserves to be #5 on your Jazz list..
Also, Duff McKagen bought a white metallic Japanese Jazz Bass Special in the mid eighties which he used during the Guns and Roses hey dey. That bass is technically a PJ on a Jazz body. I bought the same bass at the same time and while Duff became famous, I foolishly sold mine.
Maybe you need to expand beyond just four and where do the PJ players fit in?