Dear Rossinator,
Ok, what I told you is still valid, there is a common connection, the copper wire and two "signal" wires, the white and the red wires, you have to connect them to the wires coming out from the drivers, the left one and the right one. So in order to preserve the correct L & R connection, you have to connect the Right signal wire (red) to the red on the right driver, and the Left signal wire to the red wire on the left drivers, the two white wires of the two speakers need to be connected both to the common wire ( the copper common wire).
In this kind of headphones, the two metal arches have both a mechanical and an electrical role, because they assure the electrical connection between the two cups. So, pratically you should just swap the connections in the previous scheme:
you should connect the copper external wire (the shield) of your main cable to the headphones pole were is still connected the white wire in the bottom picture, and solder also the white wire in the top picture at the same point.
If the entry cable in on the right cup, next you have to sold the red wire of the main cable to the red wire of the driver in the top picture, and the white wire of the main cable to the other pole, were is connected the red cable of the bottom picture.
I hope that can help you
PS: the superlux 681 is quite similar to the 688, here a picture of the input electrical connections
So, using your picture as reference, I tried to sketch the right connections
please let me know