Ascending numerical sorting with non-numerical characters last

Try to modify your query args to this:

    $options['ind_start'] = array(
        'label' => 'Start Date (Earliest)',
        'query_args' => array(
            'meta_query' => array(
                'start_date_query' => array(
                    'key' => 'start_date',
                    'compare' => 'EXISTS', // Optional
                ),
            )
        )
    );

meta_query – will include only posts with any start_date value.

Then add a WP query order filter:

function my_order_filter($orderby, $obj){
    global $wpdb;

    // Put here some conditional logic if you want to apply this only for a specific query.

    $new_order_query_part = "{$wpdb->postmeta}.meta_value="-" ASC, {$wpdb->postmeta}.meta_value ASC ";
    if( trim($orderby) ){
        $orderby = $new_order_query_part . ', ' . $orderby;
    } else {
        $orderby = $new_order_query_part;
    }

    return $orderby;
}
add_filter( 'posts_orderby_request', 'my_order_filter', 10, 2 );

This filter will be applied to all queries. If you need to add order feature only to a specific query, then use some conditional filtering before applying the new order to the request.