Nice post.
There is some mystery surrounding the origins of jazz, as well as blues, due to a scarcity of recorded evidence until the 1920s. One point to consider is the following: the question of where jazz was born depends greatly on how we define jazz. It is possible to define jazz to include ragtime. A that case, a strong argument can be made that it wasn't born in New Orleans. If we define jazz as the kind of mix of ragtime, blues, and rhythmic nuance that Jelly Roll Morton talked about, then a strong case can be made for New Orleans as the center of its birth.
Personally, I don't have any problem with considering New Orleans the true birthplace of jazz.