>>with all theme related settings unchecked
Is it a typo ‘unchecked’? You should turn ON ‘edit_theme_options’ capability for that user role.
In case you need further help please send a copy of Canvas theme installation package to support[at-sign]role-editor.com. I will test it.
Any commercial product copy I get for testing is used at my local test environment only.
Yes, ‘manage_options’ is about site settings. It protects the ‘Settings’ menu. The most often it’s used by plugins which add menu item to the ‘Settings’ menu. So it’s just the Canvas theme’s developer choice.
Check that you did not give to the user with ‘manage_options’ much more permissions than you initially planned. May be you need to block some extra menu items with Admin menu blocking module.