So I ripped Avast completely off my server in a fit of frustration. I then installed SOA, making NO other changes to my server. Clients are deploying as I type this and successfully checking in to the SOA console. The clients (FINALLY) show avast! Administration Console in the Settings > Troubleshooting.
In fact, it even converted my standalone clients to be managed.
The only thing I can conclude is that the edu license doesn't support EAC, even though it's a download option on the EDU page and I takes the licensing file just fine.
I'm contemplating installing all the clients with SOA and then replacing SOA with EAC to see if that works. It's been quite a frustrating ride.