Loop that displays the first post of every available custom post type?

This should work for you:

// grab all public post types
$post_types = get_post_types( array('public' => true), 'names' );

// loops through each post type
foreach( $post_types as $type ) {

    // setup the query
    $query_args = array(
        'post_type' => $type,
        'posts_per_page' => 1
    );

    // perform the query
    $items = get_posts( $query_args );

    // check if we have found anything
    if( $items ) {

        // loop through the items
        foreach( $items as $item ) {

            // show the post thumbnail
            echo get_the_post_thumbnail( $item->ID, 'thumbnail' );

        }

    }

}