The suggestion above works for both Firefox and Thunderbird.
In my observation it worked best to use 'Restart [application]' rather than 'Restart Later'. They both seem to attempt a sort of background update, then revert to a full download mode. Persistently restarting and checking Help -> Check for Updates until you're all done seems to be a sure way to make it all the way through the process. This may just be the result of my battered and abused install, as LMDE has put up with a lot of my crap since it began.
Also, do not panic that your configuration wasn't carried over to the Root account, it will still be there when you open it up in the standard manner.