It seems like at some point in the past you could do that but I do not see that as an option now. Am I imagining things? Was this ever an option?
Yes, that was possible in the past. It was an ordeal that basically took manual work on the part of CS, so good luck with that these days
It requires the two accounts to own the same expansions, buying a transfer token on the character to move and then filing a request for the transfer. And waiting. of you are not in a great rush, you could request whether they are still available.
It is possible but you will need the name, address, last 4 of the last debit or credit card used, secret answer and email for the account you are moving from and you have to petition before you do anything. A CS rep told me that they no longer take the transfer tokens as a form of payment for transferring from one account to another. That may be something new or he may have been mistaken but don't buy anything until you've communicated with them because they do not like to give refunds and will make you jump through hoops for anything they do for you.