Recovery key invalid

I've been using ONE Apple ID since 2009, and I've spent over $1500 on it over the years. I activated two-step verification years ago, with ONE trusted device and (of course) the recovery key. However, two days ago, I had to reset my trusted device for various reasons, but before I did, I logged into the Apple ID webpage and downloaded the recovery key PDF. However, Apple now keeps displaying an "The Recovery Key you entered is not valid" popup whenever I try to log in with the Apple ID, password and then the recovery key I'd downloaded literally MINUTES before resetting my trusted device. I'm basically locked out of my eight-year-old account.

I have two iPhones 6, two iPhones 6S Plus (all four running iOS 10.2.1) and a MacBook Air running MacOS Sierra 10.12.3.

Is there any way around this? The recovery key is the latest one (I've only ever had ONE key before this and that one doesn't work). Please help me out.