>A practical solution, IMO, would be several organizations running and publishing the builds—i.e. several independent F-Droids. Then, a few interested people could rather trivially automatically download the binaries and compare them. If one of the ‘stores’ gets compromised, a mismatch in binaries would indicate that.

This idea has been discussed for years in the reproducible builds project. There has been some progress on this part on the Debian side of things, and you can in practice deploy rebuilders and make APT communicate and compare signed attestations.

Lukas from NYU did a presentation during miniDebConf in June. https://www.youtube.com/watch?v=hbHa4OFv7Qo

Disclaimer: I worked on this project and contribute to the reproducible builds project.