I share your interest but notice you don't mention Cuba, which has to have had influence, the rhythms inherited by jazz have to have origins in African rhumba, imported to Cuba and other places in South America from Africa, then imported to New Orleans, since there has always been an influx of migration from less economically well off Cuba to nearby better off New Orleans, since folk of color had freedom to do that.
There are written records and painted artworks of Cuban salsa musicians and bands improvising with all kinds of instruments including wind, to produce what might have become early jazz, going back to maybe 1850, but we can only imagine what that must have sounded like unfortunately, unless there might be forms of it preserved by cultural folkloric bands in Cuba that still faithfully reproduce the sounds and rhythms that existed before recordings became possible. There are cultural folkloric bands in Cuba that might know something about that. It would be interesting to know :)