Update: "index_home" is not used for the home page; that and all other index pages are named "index", so there is no way of distinguishing the home page with the page-name subfolder system.
This is obviously a potential problem, and ought to be changed, but the change would be deep in the core code.
You would need to customize the basic template copy of tpl_main_page.php with
PHP Code:
if($this_is_home_page) {
//do homepage stuff
}else{
//do standard stuff
}
to execute one thing on the home page and another on other pages.