I think Zhondra and the drummer were differetn characers, but performed by the same person, fran brill.
While, very few re-appeared, they did have names: the keyboard player was digit, who had a bigger role on the show as the technical director (and he was seen again, in the cosby show episode "cliffs nightmare", as the host of the "shart circuit" mini-game in muppet party cruise, and although I don't remember him in the scene, I have heard that he made a brief appearance in muppetvision 3D, at the beginning of the muppet labs segment). the saxaphone player was named flash. the guitar player was named beard, and although he never appeared again, he looks similar to zeke, from the jugband. clifford played base guitar. the only member who didn't have a name (as far as I know, and I am not sure if the fans know either) was the drummer.
I haven't seen much jim Henson Hour either, but they were better developed than the muppets tonight band. I think they were the focus of the musicians episode, and uite a few of them interacted with other characters on a regular basis. since digit worked backstage, he regularly interacted with the cast, and was one of the main characters on the show (he was one of dave goelz' main characters, in addition to gozo). clifford often appeared backstage in many episodes. beard was also seen backstage in quite a few episodes, like food and the secrets of the muppets.