Help with show_option_all and show_option_none for taxonomy dropdown

I am using a drop down box (populated by custom taxonomies) to allow users to search CPTs.

Everything works fine except I can’t get a “choose all” type option to work or a “select a TAXONOMY NAME” default option to show.

I am using get_terms_dropdown to populate the dropdown. I have successfully used show_option_all and show_option_none with wp_dropdown_categories so presumably it is just weak php skills that is the problem.

Below is my code – without show_option_all or show_option_none. I am hoping some can help me either:

1) integrate those two commands into my code, or

2) a different way to create a taxonomy dropdown

<form action="<?php bloginfo('url'); ?>" method="get">
<div>
<?php
$taxonomies = array('TAXONOMY NAME');
$args = array('orderby'=>'name','hide_empty'=>true);
$select = get_terms_dropdown($taxonomies, $args);

$select = preg_replace("#<select([^>]*)>#", "<select$1 onchange='return this.form.submit()'>", $select);
echo $select;
?>
<noscript><div><input type="submit" value="Näytä" /></div></noscript>
</div></form>
<?php
function get_terms_dropdown($taxonomies, $args){
$myterms = get_terms($taxonomies, $args);
$output ="<select name='TAXONOMY SLUG'>";
foreach($myterms as $term){
$root_url = get_bloginfo('url');
$term_taxonomy=$term->taxonomy;
$term_slug=$term->slug;
$term_name =$term->name;
$link = $term_slug;
$output .="<option value='".$link."'>".$term_name."</option>";
}
$output .="</select>";
return $output;
}
?>