If you are still ordering by a single meta field you can still to that without a lot of work. I think this will work.
$byartist_args = (array(
'numberposts' => -1,
'post_type' => 'Event',
'meta_query' => array(
'relation' => 'AND',
array(
'key' => 'artist',
'value' => get_the_ID(),
'compare' => '=',
),
array(
'key' => 'event_date',
'compare' => 'BETWEEN',
'type' => 'DATE',
'value' => array($date_1, $date_2),
),
),
'meta_key' => 'event_date'
'orderby' => 'meta_value_num',
'order' => 'ASC',
'nopaging' => true
));