A history of the 1st Missouri Cavalry (CS) was published a few years ago. The author's name is James Farley, and the book is called Forgotten Valor: The First Missouri Cavalry Regiment CSA. I haven't read this one, so I can't say much about it. I got the impression that it was largely based on secondary sources, but not having read it I may be completely off base there. Did hear the author speak about the book at a roundtable right after it came out, but that's been awhile.

Gottschalk's book, In Deadly Earnest, does spend some time with Green's Brigade at Vicksburg, although his focus is obviously on Cockrell's Brigade.

Jim McGhee probably would have some suggestions for you as well.

Hope this helps.