Replacing Gallery Shortcode with Foundation's Clearing

Using wordpress 4.1 and Foundation 5, and attempting to replace the stock gallery shortcode with foundation's clearing.

In debugging mode, I get a notice of:

Strict Standards: call_user_func_array() expects parameter 1 to be a valid callback, non-static method foundation_clearing_gallery_replacement::init() should not be called statically in ../wp-includes/plugin.php on line 496

And whenever I save a page/post/etc, only in debugging mode, I get the white screen of death with a "cannot modify header" information on similar line.

The opening of my plugin, which is where I think the problem is manifesting, is:

class foundation_clearing_gallery_replacement {
    function __construct(){
        add_action( "init", array( __CLASS__, "init" ) );
    }

    function init(){
        remove_shortcode( 'gallery' );
        add_shortcode( 'gallery', array( __CLASS__, "gallery_shortcode" ) );
    }

With the ending line:

new foundation_clearing_gallery_replacement();

Full source can be seen here