Sorry to read that you're unable to watch TV Anywhere on your iPad even though it is registered.
I appreciate the checks you have already done so far. As you have one device change available, if you can sign into your TV Anywhere account from a laptop/PC, on the right hand side under My Profile select Device Settings. Within here you will see the iPad and remove the device from the list. Once this is done, go back on the app on the iPad itself, select a channel to stream as this will prompt for registration.
Hopefully this will then work for you. Let me know how you get on.