Problem solved - I got it!
After making my initial post, I went back to my DAW and tried again. This time it worked fine and registration is now complete.
So as usual, the problem was between my ears: I must have been inputting the registration code incorrectly.
Thanks to all who replied, and sorry for the pointless post.
And yes, I really am Elton John (just not the one who wrote all those famous songs).