Oops, wrong video, my bad.
That drummer is identifiecd as one Tony DeNicola.
Also, the second of those tenor players is Jay Corre, who went on to play in Buddy's first post-James band. a very agreeable player imo.
The video with Buddy is this one. Recommended to watch the entire thing, because they cover a lot of bases before they're finished, all of it within their own zone. Stay tuned for the electric piano solo. In 1965!
As far as CD recs, I would think that the two Verves listed above are probably going to be the only available issues of quality for this era.
Same(ish) band, Tokyo, 1964
I would point out that the book is not a rehash of 30s-40s sounds, even when the songs themselves are (when they are). It's the type of thing that won't scare off any old listeners, and yet won't run off slightly more "modern" (relatively) ears.
Plus, having a home base in Vegas meant steady employment for the players, as well as ongoing commissions for writers.
The Harry James band was pretty stealth, actually.