[Fixed!]
They've changed the behaviour. It is now necessary to add in a sum for Cost Per Order. You can make it what you like (I added in 0.50) and then deduct that amount from the Flat Rate Shipping Options you've set up in the Additional Rates box and it should all work.
So for example:
You want
Europe Shipping to be 5.50 and
Courier to be 10.00
You set up:
Cost Per Order: 0.50
and add the following to the Additional Rates box:
Flat Rate Shipping Options:
Europe | 5.00 | order
Courier | 9.50 | order
Once you've done this, the shipping rates magically appear in the Cart and Checkout as they used to.
They clearly need to document this asap.