I have three custom taxonomies, Genre, Type and Ayear, with multiple terms in each. How can I create a multiple Drop-Down that lists all the terms for each custom taxonomy that a user can filter when they hit a submit button?

I found this code snippet and it works partially, but when I hit submit, it returns the terms id's rather than the slugs. So I get www.site.com/?genre=6&type=5&ayear=3
How can I get it to return, www.site.com/?gene=action&type=new&ayear=2009

Code:
function my_dropdown($name, $taxonomy = 'category')
{
    $defaults = array(
        'taxonomy' => $taxonomy,
        'id' => $name,
        'name' => $name,
        'show_option_none' => ' - Select - ',
        'selected' => get_query_var($name)
    );
    
    wp_dropdown_categories($defaults);
}

add_action('pre_get_posts', 'my_customsearch');
function my_customsearch($query)
{

    
    $tax_query = array();
    $genre     = (int) get_query_var('genre');
    $type      = (int) get_query_var('type');
    $ayear     = (int) get_query_var('ayear');
    
    // first dropdown
    if (!empty($genre) && $genre > 0) {
        $tax_query[] = array(
            'taxonomy' => 'genre',
            'field' => 'slug',
            'terms' => $genre
        );
    }
    
    // second dropdown
    if (!empty($type) && $type > 0) {
        $tax_query[] = array(
            'taxonomy' => 'type',
            'field' => 'slug',
            'terms' => $type
        );
    }
    
    // third dropdown
    if (!empty($ayear) && $ayear > 0) {
        $tax_query[] = array(
            'taxonomy' => 'ayear',
            'field' => 'slug',
            'terms' => $ayear
        );
    }
    
    if (sizeof($tax_query) > 0) {
        $tax_query['relation'] = 'AND';
        $query->set('tax_query', $tax_query);
    }
    
}

// add my custom query vars
add_filter('query_vars', 'mycustom_query_vars');

function mycustom_query_vars($query_vars)
{
    $query_vars[] = 'genre';
    $query_vars[] = 'type';
    $query_vars[] = 'ayear';
    
    return $query_vars;
}
Code:
<form role="search" method="get" id="searchform" action="<?php echo bloginfo( 'url' ); ?>">

<?php echo my_dropdown('genre', 'genre'); ?>
<?php echo my_dropdown('type', 'type'); ?>
<?php echo my_dropdown('ayear', 'ayear'); ?>

<input type="submit" id="searchsubmit" value="Submit" />
</form>