The key comment is this: "We are also considering ways to get the people most interested in going to those editathons to also run them (empowering them, in effect)."
If edit-a-thons are to achieve scale, it's necessary that once established, the group will continue under its own momentum. This frees up the original organisers (or new members who have "graduated" to become new organisers) to move on and establish similar groups.
Just an aside, I think we need a different term for this kind of regular edit session. Perhaps it's just my own cultural baggage, but I associate the "-a-thon" as a big once-off event e.g.
https://en.wikipedia.org/wiki/Wikipedia:Meetup/Canberra/2014-08-14-Wikibomb
rather than something smaller but more regular and ongoing. Maybe we should call it an editfika :-)
Kerry