Helene survivor here. I will be spreading the word about this project and keeping some APKs for if the shit hits the fan again. FDroid being able to sync between local devices means all you need is to get fdroid onto someones phone. Wish they had an iphone app though!
Doesn't Briar itself provide functionality to share the apk via Bluetooth? So you don't even need F-Droid (though it's still good to have regardless, of course).