Here's an update on the current situation:
There aren't any members of the New Team who currently have server admin know-how, but there
are several who have shown bravery at learning as they go along, so that provided us with an opportunity.
I'll handle installing/configuring/transferring EQFA to a shared hosting plan that the new mods are signing up for. Once that is in place, the new admins/mods should be able to then take over the tiller and keep the site afloat. Performance on a shared host won't be quite as good as having your own Pocket-Kael, but Dreamhost probably won't want to retire in a few years, so it's a more reliable and stress-free choice for all involved.
The transfer should happen over the weekend, so don't be shocked if the site is unavailable. I'll attempt to keep a status page active.
Once the new site goes live, there will probably be hiccups for a few weeks, and new steps to learn for uploading art and the like. (It will be more like EQFA 1.0, which some of you may remember.) But if everyone is patient and supportive, I'm sure things will continue to chug along just fine.