Not sure if this would help, but I recently learned about a product called iMazing[1] that lets you browse and edit iTunes backups.
You can't access the whole filesystem of a running iDevice with it, but you can access the whole filesystem of the backup. So I suspect it might be possible for you to clean-up the backup offline & then restore it. (At a minimum it should enable you to extract the valuable contents out of the backup and manually restore it on top of a clean iOS install.)
I've used it with some success to extract info from the photos database. I just wish they had a consumer-facing (read: more affordable/perpetually licensed) version of their CLI tool.
You can't access the whole filesystem of a running iDevice with it, but you can access the whole filesystem of the backup. So I suspect it might be possible for you to clean-up the backup offline & then restore it. (At a minimum it should enable you to extract the valuable contents out of the backup and manually restore it on top of a clean iOS install.)
I've used it with some success to extract info from the photos database. I just wish they had a consumer-facing (read: more affordable/perpetually licensed) version of their CLI tool.
[1]: https://imazing.com/