While I'm not as stuck on N'orleans as Rok is, we share Dr. John, and I know where he's coming from.
I'm familiar with all the musicians on your list, except I have yet to get into Andrew Hill.
Since I feel like I'm "short-timing", I don't even bother with any of the latest music. I've known a number of jazz musicians personally (not that many) and all of them were raised in one of our fantastic cities that no longer exist. You grow corn in a corn field; if there are no more corn fields, where can you grow corn?
You grow "Jazz musicians" in cities, if there are no more cities (not places out of a science fiction movie, Detroit for example) where can you grow Jazz musicians?