instead of hooking in the secondary navigation and dealing with a whole bunch of different HTML and Customizer settings as well as GP hooks, the simplest option maybe to swap the Menus using this PHP Snippet:
TLDR:
Are you using a Child Theme?
If Yes, then you can add the snippet to your child theme functions.php file
If No, then use the Code Snippets plugin ( link in the above doc ) and add it to a New Snippet.