I sort of figured out a way to do this.
- Add a variant within the Panels module
- Add a visibility rule so that different variants show at different URLs (clean URLs and paths required), for example, example.com/paneltitle/variant1, example.com/paneltitle/variant2.
- Create a custom module to hook into the menu. There is a great example of a menu module in the module code samples on drupal.org.
This seems to have worked for me.