Sorry, but Sync wasn't intended to be used in that manner - IOW, as a backup medium when you reinstall your operating system. Sync is intended to be used to synchronize your Firefox data across multiple devices.

Too many users fail to realize that the Firefox Account (FXA) Password is the encryption "key" for their data; change that "key" for any reason and the data sitting in the Sync server is useless - it can't be decrypted. So when a new FXA Password is requested the users data is wiped from the Sync server to give them a fresh start without needing to create a new Firefox Account with a different email address (the primary identifier).