Since F-Droid (i.e., the repositories, not the app) builds all apps, a practical solution would be for the repositories (i.e., their signing keys) to be recognized by El Goog. Whether and how much help / obstacle the "maybe we do evil" company puts up for / against this is a different question.
The Emacs version for Android makes uses of something like this IIRC by signing a version of Termux with the same key and distributing it in the same SourceForge repo such that Emacs on Android can access CLI tooling like git for example.
jjice · · focus · HN ↗
pritambaral · · focus · HN ↗
rom1v · · focus · HN ↗
aquariusDue · · focus · HN ↗