You can center the logo on menu easily using 2 additional menus. You need to register two separate menus in Genesis and show them on both sides of the logo. Its simple in genesis and You can use this code snippet in Function file or in Code snippet plugin.
Here is what it looks like once you register the menu and create a menu for both locations.
Small CSS work may be required depending on different themes.
Or you can download this file and import in code snippet plugin.