I think I have solved this issue. What I did was uninstall Firefox using Revo Uninstaller with the post-uninstall scan set to "Advanced" to make sure it removed everything. Then I downloaded a fresh copy of the Firefox installer and tested it before signing in to my account (which automatically downloads all my add-ons). Once I was sure everything was working without the add-ons, I updated my Macrium Reflect disc image backup and then signed in to Firefox and tested it again when all the ad ons had been installed. I hope it's fixed now.