Any national GLO that goes on a campus will start by building an interest group around 20. It seems daunting, but it's not that hard the way they do it. I'm not saying all 20 of them will stick around long-term, but they create a foundation to move through that re-building phase. They have a lot of work ahead of them and they need help to share the load.
As far as alumni... I don't really know what to say. It's not a national GLO, so there's no power structure that gives a theoretical alumni board authority over the chapter. If there was, then sure they could step in & forcibly throw people out &/or order changes. If they had no alumni involvement, but a national HQ then national would step in to do that stuff. As it is, all they could get from alumni is a glorified pep talk.
I'm not saying that's bad, but it seems unrealistic to get the people to even do that. With a 22yo org, those alumni have kids, jobs, mortgages, etc consuming the majority of their lives. Finding a group of people that can be deeply involved would be difficult, and I don't see that their powerless involvement could necessarily turn the tide.
So, I wouldn't count on alumni. I wouldn't waste time with the stupid interpersonal issues. I'd just clean house to get back on message. Then go find a bunch more people to get this thing back on its feet.
A national expansion team would be down there looking at non-greek folks in student govt, other orgs, RAs, intramural teams... you can string a lot of people together that bring different strengths to the equation. And watch all these videos:
http://www.ato.org/Undergraduates/re...cruitment.aspx