Unfortunately, once the transaction has posted in the wrong account, either a journal entry or editing the unmatched transaction in the bank feed seems to be the only correction available.

 I may have stumbled on the answer but still need to test it. We recently changed bank accounts and had the same issue. Bill Payments posting the the wrong account register even though we made sure the correct account was selected throughout the process of selecting the bills and scheduling payments. I have attached a couple a screen shot that may be helpful.

1) When you get to the first Bill Payment screen, confirm the correct bank account and select the bills you want to pay.

2) In the next window, again confirm the correct bank account, but also click on "select account"

3) This will bring you to a pop up window to actually select the account. Just to the right is a drop down window showing were the transactions should post in QuickBooks. Edit if necessary. (It does seem the system will remember the selection for the next time you pay bills)