Initial letters with a manually inserted language switcher

You can use mlp_get_interlinked_permalinks(). It returns an array with some data about the translations, so you can create your own HTML output.

The key is the ID of the blog, the value is an array with these values:

'post_id'    => integer,
'post_title' => string,
'permalink'  => URL,
'flag'       => URL,
'lang'       => string

Something like this could work, not tested! I have no time for more, sorry.

In your theme’s function.php:

function get_translation_navigation()
{
	$links     = (array) mlp_get_interlinked_permalinks();
	$login = new stdClass;

	if ( is_user_logged_in() ) {
		$login->url = wp_login_url( $_SERVER['REQUEST_URI'] );
		$login->text = 'Log in';
	}
	else {
		$login->url = wp_logout_url( $_SERVER['REQUEST_URI'] );
		$login->text = 'Log out';
	}

	$html = '<ul class="lang-nav">';

	foreach ( $links as $link ) {
		$html .= sprintf(
			'<li><a href="%1$s" hreflang="%2$s">%3$s</a></li>',
			esc_url( $link['permalink'] ),
			esc_attr( $link['lang'] ),
			strtoupper( strtok( $link['lang'], '_' ) )
		);
	}

	$html .= '<li><a href="' . $login->url . '">' . $login->text . '</a></li>';
	$html .= '</ul>';

	return $html;
}

In your template call that function like this:

print get_translation_navigation();