Hi there,
my thinking would be this:
1. Add a Logo to the Site Header as you would want it displayed for the internal ( not home ) pages.
2. Set the Customizer > Layout > Primary Navigation location to Below Header
3. Create a Header Element for your Front Page:
https://docs.generatepress.com/article/header-element-overview/
For its content you can include the heading and sub-heading.
Then go to the Site Header tab of the header element where you can select Merge with Content and change the Site Logo if you wish.
4. Now we need to position the Primary Nav below our Header Element by adding this PHP Snippet to our site:
add_action( 'after_setup_theme','craig_move_navigation' );
function craig_move_navigation() {
remove_action( 'generate_after_header', 'generate_add_navigation_after_header', 5 );
add_action( 'generate_after_header', 'generate_add_navigation_after_header', 15 );
}