Please help me out with one question. Instead of explanation, I will try to show examples for better understanding.
If for example, I want my home page’s main menu and header to look something like this: http://themes.themegoods.com/letsblog/demo/
I also would like to see how the crew addresses this need. It seems like there is no easy option for this. If you are comfortable writing code, this could be easily solved by writing custom css to your specific design needs along with some WP conditional tags. A few filters that might help you set/unset CSS classes and set position of the navigation: generate_navigation_class, generate_navigation_location, and the core body_class filters.
If writing custom code is not your thing, and you are using a page builder plugin, you could also disable the header on some specific pages, and build a custom header from scratch using page builder for these pages.