Well, I just put my nose to the grindstone and figured it out for myself, so here it is for anyone who needs it.
If you want to pump values about the order into the checkout success page, there's a global variable available in the page editor section called $orders. It's an object of the queryFactorResult class and contains an array propert called fields which has a whole mess of data you can use. For example:
<?php echo $orders->fields['orders_id']; // The order ID ?>
<?php echo $orders->fields['order_total']; // Total amount of order ?>
I am not sure if order_total includes shipping or not, so check on that if you need to break it down, but there's a start. You can just var_dump($orders) to take a look at the whole object when you do a test sale.