Checkout page change theme
In a custom module you can change the theme like this:

function YOUR_MODULE_custom_theme() {
  if (current_path() == 'checkout') {
    return 'plain';
  }
}


With this approach you need a full new theme (in the above example named plain). You then can directly use it's page.tpl.php. In template_preprocess_page you could add javascript and fill variables with your html (or blocks).

Also you can place the blocks like you want for this theme.

To get the correct current_path you would need to debug a lil. checkout is just guessed by me ..