1. Advanced Template Manager
My first suggestion here would be the Advanced Template Manager by Regular Labs.
It gives full control on how you can assign templates. It covers Joomla content by articles, categories, page types... or for you case, the pro version provides option to assign template by User Groups or Users IDs.
So for example, you could set a specific template for your members/registered users.
Note: Test the free version first to see if it works well with gantry5, before deciding to go for the Pro version.
2. Be creative with core template manager
Alternatively, using the core template manager this is another idea that could work (depending on how your whole website is configured).
Set as default template the one that you want to assign to those pages that don't have a menu item, and then assign your other templates on those pages that have a menu item.
3. Custom Plugin
Finally, there is the custom route. Create a simple system plugin which will detect the category of the current page - you could use something like the
onAfterInitialise event - and set the desired template according to your liking. You could even check for the current user/usergroup - or mix both category and user checks.