You can try removing the document ready part of your jQuery if you deploy a HTML snippet on each page.
This way the snippet should be executed immediately instead of waiting for a document ready event.
The HTML snippet should load after the menu – in this case it should work:
$(".bottom-menu-navigation li").eq(0).addClass( "active" );
You can also use a dirty alternative of creating a different layout for your main navigation pages which need different active tags and adding a menu item with a hardcoded class for each page.