With the free version of Admin Menu Editor you can only make menu permissions more restrictive, not less. You'd have to use the Pro version (or a different permissions management plugin) to make the Custom Header menu accessible to editors.
This limitation is a side-effect of how menu permissions work in WP. In addition to the required capability set for the menu (which you can change with the free version of the plugin), most admin pages also contain another, hard-coded capability check. The user has to pass both checks to access the page. As a result, it is not possible to make menu permissions less restrictive just by editing the required capability. You can only restrict them further.
The Pro version deals with this by automatically granting the necessary capability to the selected roles and enabling them to pass the hard-coded checks.