Well, my theory that you had to be in the same region didn't immediately bear fruit as I found out yesterday. However, this evening when I logged onto Beta I spotted a new drop down menu at the top of the character copy window in game where you can select region.
However after several minutes it is still sat with the "Copy in Progress" window open and nothing is happening. Hrmph!
So looks like, at least for me, the character copy is still not working :(