How to migrate app data when switching the app source

Say I have "FunnyApp" installed from Playstore, now it turns up at F-Droid – and I want to replace the Playstore version by the F-Droid one (same issue vice-versa). Trouble is, I cannot simply update the app from the new source as the signature doesn't match (F-Droid signs with their own key). FunnyApp doesn't offer any "export" functionality, but I don't want to lose its data. **What would be possible approaches to perform a proper switch?** Traps: * Simply updating/installing from "the other source" does not work (signature mismatch) * performing a data-only adb backup doesn't help, as the restore will fail for the same reason I have some vague ideas on root-based solutions which I haven't tried yet (e.g. Titanium Backup might be able to restore data despite of the changed signature, and there's also some XPosed module (InstallerOpts?) offering to "suppress the signature warning"). But before "messing up big" I thought to ask here if someone might already have successfully tried some solution. Non-root solutions preferred (so more people can profit from), root-based solutions acceptable, XPosed as requirement OK as well. ---- Some reasons why one might want to "switch sources" (aka "cross-update"): Getting rid of proprietary dependencies, app no longer updated at original source …