Dusty's call of Bonaparte's Retreat sounds right to me. If memory serves, I think I heard Don Pedi say some years back that he thought that "snake charmer" part was a later addition to the tune.
Great video, Dan-- so glad you shared it!
Bonaparte's Retreat, methinks.
Edit: Today people usually play Bonaparte's Retreat with three parts. The version in the documentary only has two of them. The missing part is what defines the tune to us as mixolydian since it relies on the lowered 7th. If you skip that part, you can probably play it in either ionian or mixolydian.