Is there a way I can create a backup of my current layout?
I'd like to try one of the templates to see if it is going to look right with our setup, but I want to be able to go back to what we have if I decide I don't like it.
It's actually pretty well built in that you can roll back. It's especially easy for you since you're just using the default layout: after deploying the new template, if you don't like it, you can click the "Disable both Advanced Layout and Custom CSS" button, which will more-or-less roll you back to your previous config.
Alternatively, a complete history of your CSS is kept, and also a complete deployment history of amny custom advanced layouts. So there's almost always a way to roll back.