Tried a second time to pay with PayPal, which accepts the transaction: however the confirmation page displays an error, saying to contact sales, and the form to contact sales ends up throwing up another error.
Now my credit card payment is in a indeterminate state, while the PayPal payment got through but I wasn't given a license key and there does not seem to be a reliable way to get one.
Luckily I still have my license for the previous IntelliJ version, it looks like I will use it for quite a while.