Well, great news for you since Mozilla has changed their Sync protocol mechanism in the latest version which was released last April (Firefox 29). The new system only requires you to sign up using the new Firefox account and it's password-based system (two-factor authentication is now being developed, with a possibility of using Google Authenticator App and SMS).
Here are the easy step to migrate to the new sync protocol:
- upgrade everything to FF29
- disconnect old browsers from Sync
- create a Firefox Account
- sign all browsers into your new account with the same email and password
For those who are still using the old sync, please note that they will end the old protocol at the end of ESR release maintenance period (14-Oct-2014), so what are you waiting for? Upgrade now :)
Here's some warnings:
pairing-based Old Sync and password-based FxA-powered New Sync don’t mix: if you used pairing to connect two FF28 browsers together, you won’t be able to connect a third FF29 browser to them, even if you upgrade them all to FF29.