RE: 100 year old Rumba
As nloftofan1 said, no one danced international Rumba a 100 years ago. If you can settle for a few decades less, I have a suggestion.
"Quireme Mucho" translated into English as "Yours". It was written by Gonzalo Roig (Havana, 20 July 1890 Havana, 13 June 1970) who was a Cuban musician, composer, musical director and founder of several orchestras. He was a pioneer of the symphonic movement in Cuba. (Source: Wikipedia).
This song was very popular, world-wide in the 1930s or 1940s.
It is beutiful romantic song with simple but expressive words. Many famous performers, including Placido Domingo, Jose Carreras and Ray Charles sang a version of it. Linda Ronstadts version (Spanish) is danceable and occasionally, but very seldom, used at Rumba shows. I have not heard it at competitions. Maybe, because the beginning is not a clear Rumba and because the tempo is rather slow.
Listen to the various versions, one may work for you. Ravel's Bolero suggested by nloftofan1 would be an interesting choice as well.
Please let us know what your choice is, and if the audience liked it.