You've got the right idea, except your array should look like:
$requestArr = array(
'subscription' => array(
'customer_id' => $thisCustomerID,
'next_billing_at' => '2013-04-20'
)
);
and then you should be good (tested)
reference: http://docs.chargify.com/api-subscriptions#api-usage-json-subscriptions-update