News Flash: Mail-in payments are accepted. They must be sent to GS Bank at their Salt Lake City Branch. Strangely enough, the address they gave me over the phone is the SLC Branch, but with a Pennsylvania address.
They say that the payment may not necessarily post on the date of receipt, but will be backdated to the date of receipt. It may take some time before the funds clear and reflected in available credit.
OP's BT would have worked if sent to the correct address.
As the premise of the topic has been fairly well-covered in the original thread, this thread has run its course and is now locked/merged and closed to new messages.