So would this work, you have module called my-module-does-something and you assign it a module position of mymoduledoessomething.
Then you create an article, which isn't tied to a menu item, and then in the article have this HTML code ->{loadposition mymoduledoessomething}
On your Front page, you create a link that calls your article which uses loadposition to place your module on the menu-less page.
wpd93