Hello Meghan,
This is a good question especially with all the work you have been putting into customizing your Method Screens. As you have likely figured out, there isn't really any way for you to backup/download the screens to be saved offline, you can only work with them directly through Method. I really haven't heard of any Customers loosing screens they have customized or not being able to access them. Method also keeps backups on behalf of our Customers, so if something were to ever go wrong with your screens, technically we would be able to restore from an older backup on request.
If anything, I would suggest maybe making a copy of your Custom screens, this way, if anything happened to them, or you made a change that messed things up, you could always default to your backup screen.
-Ben