I doubt that Dootone was a major force (except perhaps for a few r&b singles and a bunch of comedy records) outside of the L.A. area. I believe that Dootone recorded only Dexter, Counce, Perkins, and Collette. Perhaps Dootsie Williams gave up on jazz before he got around to Teddy Edwards. By 1958, he was making his money from Redd Foxx and similar comedy records.
It's hard for me to ignore the strong possibility (fact?) that race played a big part in the west coast music business and that had Teddy Edwards been based in New York, he most probably would have been more visible on records.