An action that runs after each post in the loop on index/archive page?

I am not aware of a dedicated action, but you could prevent double processing with an internal cache in your function.

Pseudo code:

function content_filter( $content )
{
    static $cache = array();
    $id           = get_the_ID();

    if ( in_array( $id, $cache ) )
    {
        return $content; // we did this already
    }

    $cache[] = $id;

    return $content . 'your awesome extra';
}