@nalexander about Google Play Services, what is the push stuff used for? I never understand why Firefox needed its own push services. But I do understand why push requires GCM on Android.
About reproducible builds, check out
fdroid verify and our verification server:
The process is not well documented, but there are currently two ways to get APKs into f-droid.org via reproducible builds:
fdroid signaturesto get the APK signature from a release APK, then add that to fdroiddata
Binaries:field which has a link to the releases that f-droid.org reproduce https://f-droid.org/docs/Build_Metadata_Reference/#Binaries
Happy to help you try that stuff out. Perhaps that would be better in a new thread.