The short: is there a way to have a git repo push to and pull from a list of remote repos (rather than a single \"origin\")?
The long:
You'll need a script to loop through them. Git doesn't a provide a "push all." You could theoretically do a push in multiple threads, but a native method is not available.
Fetch is even more complicated, and I'd recommend doing that linearly.
I think your best answer is to have once machine that everybody does a push / pull to, if that's at all possible.