Possibility to echo the menu?

You could use something like this in your function.php, example for one menu, it is copied including events and appended to #primary:

function my_copy_jsrm() {
?>
<script type="text/javascript">
jQuery(document).ready(function() {
	jQuery('.jquery-responsive-select-menu').clone(true).appendTo('#primary');
});
</script>
<?php
}
add_action( 'wp_footer', 'my_copy_jsrm', 999 );

Ditto! This would be the simplest way to accomplish this.

Thank you!