Is that possible/feasible?.
There’s no problem upstream as I’m contributor on both projects.
The rationale with KOReader change is in https://github.com/koreader/android-luajit-launcher/issues/304. Changing the package name would prevent signature problems and the main package listed in F-Droid client when it gets updates from a different channel. Sadly I didn’t think about it when we implemented the changes required for inclusion: https://github.com/koreader/koreader/issues/2040
In the case of Coolreader some changes are needed to remove GMS from the fdroid build: https://github.com/buggins/coolreader/issues/284.
In both cases the change would be the same: append suffix .fdroid to the package name:
org.koreader.launcher -> org.koreader.launcher.fdroid
org.coolreader -> org.coolreader.fdroid
Both apps keep their inner settings in the filesystem, so the change on the package name wouldn’t prevent users to repurpose their settings on the new package.
I’m aware that things could be a bit difficult. Users would need to uninstall the APK or install the new one and have two different copies of the same problem. No idea about infrastructure/metadata/etc.