(Note 6/3/24: I’ve written a follow-up to this post; the link is at the end. My reconstruction stands.)
I picked La Russe out some time ago while looking for easy late nineteenth century waltz-time variations. The name means “the Russian woman”, and I recently had the pleasure of teaching it in Moscow to a very talented group of Russian dancers.
No specific choreographer is known for La Russe, but we can date it with unusual precision to just over 130 years ago. Dancing master M. B. Gilbert, in his Round Dancing (Portland, Maine, 1890), noted that it was “introduced by the American Society of Professors of Dancing, New York, May 1st, 1882,” and it turns up in a couple of other American dance manuals of the 1880s. All the descriptions are quite consistent, though the terminology used varies.