Hi justasiam,
Apologies for the late reply.
You just need to enable debug option in plugin settings.
Once you have done that, try to place an order at the cart page. You will see the request and response information. Copy this info in a link and send it to us. Also remove any sensitive data pertaining to your account from the data as this is a public forum.
Note : The request and response will not show for Flat rates as these rates are not from our plugin but are normal woocommerce configured rates.
As soon as you provide the info, we will analyze and get back to you immediately.
Let us know if you have any query.