two points
1) In my earlier post when I mentioned Firefox I meant Thunderbird
2) Why does the profile need to be restored? Uninstaling Thunderbird does not uninstall the user profile so there is no need to restore it. In fact, if we work on the assumption that the profile is corrupt and is causing the problem, all you are attempting is to back up and reinstall a corrupt profile.
it seems to me that what needs to be done is first for for the existing mail folders to be backed up by copying or exporting (and I mean physically coped - not backed up using some arcane compression algorithm that stands a good chance of not working). The Thunderbird to be totally uninstalled and for the user profiles to be removed (or moved so they can't be "seen" by the program.
Then Thunderbird reinstalled and a new profile created. Then finally import the mails back in