In addition to my Desktops, I am using Everdo on my mobile phone. First of, I think it is a great app.
I am running a pure AOSP build without play services. The app itself works perfect also without any google services, which is awesome.
So currently I am downloading the builds from the forum, where i need to keep track an check for updates manually.
I think it could fit a great part of the actual target audience when providing a dedicated F-Droid repository. This way, we could have automatic updates, instead of the manual untrusted install.
Here is a link, how to set it up and a further description:
Please note, that it is possible this way to distribute built apk, without providing the source code.
kind regards, Stefan