Here's what we used to do in a little piano club I used to belong to here where I live, so that everyone was involved, but it wasn't a competition. We'd collectively contribute to a large performance project once a month, so each person would each be assigned one movement of a Sonata, or one Chopin prelude, for example. Sometimes these were just performed for ourselves in the group, and other times, the classical radio station would come record and air it.
This kind of thing might be an idea to fill the gaps of needed recordings on this site, but, the problems we had in the group here were that some pianists despised (sorry, Monica! I love F.C. too) Chopin, for example, so didn't want to learn him, or did but then played him poorly, which upset the other group members. Or certain members would feel insulted when they were assigned what they deemed to be one of the easiest of the Preludes, for example. "What! Oh, I see, the leader of this project gave me this piece because he/she thinks that my pianistic abilities are so poor I can only handle THAT piece?!". Ay, Karumba.