Here at USC we just use a slightly modified script to extract all the private repos for a given assignment to a local MacBook, run the MOSS perl script on the MacBook and then view the results on MOSS website.
I have a script that works to pull source files from student projects and organize them in a format that MOSS will take here. I currently haven’t had time to parameterize input to make it language agnostic so right now it just grabs .java files. I can’t speak to the GitHub Classroom roadmap, not my team, but this script works pretty well for getting student submissions to run through MOSS.