It has become clear to me that the CPR idea redacted below is waaay too complex to succeed. The less ambitious "Journal Club" idea of 2 years ago was enthusiastically received, then fizzled. I feel that was too ambitious also.
More realistically, I would propose that there can be questions based on particular papers, preprints or articles that can only be sensibly answered if that paper has been read. Perhaps with a research-paper tag? The question can be as basic as "what do you think of this paper?".
This could achieve some of the goals of a "Journal Club", such as providing higher level content, without the off-putting procedural overhead.