You can not use the st7971 shifters designed for 10 speed Dura-Ace Di2 on the 11 speed Di2. The 11 speed Dura-Ace Di2 has more in common with Ultegra than 10 speed Dura-Ace. Ultegra and 11 speed Dura-Ace uses etube and provides the signal for the shifter down the power line, this is why it only features two wires.10 speed Dura-Ace Di2 has a separate power and signal which makes them incompatible.
This is why Replacing the battery on 10 speed Di2 is not exceptionally difficult as you only need to refer to the wiring diagram which features in this thread (and understand it), Undertaking a custom battery for Ultegra or 11 speed Di2 is vastly more complicated and simply replacing the battery does not work.
10 Speed Dura-Ace has no intelligence what so ever, it has no awareness of the components in the system which is what makes it so hackable, as long as you can send a signal and power the device you can connect it to the system. 10 Speed Ultegra and 11 Speed Dura-Ace have awareness, it functions a little like a computer network in the sense that each component has awareness of the others, it is this which makes it less hackable. The fact the protocol dictates that the signal and power line is shared ensure that you can only replace items with parts which have this capability. Standard electrical switches in general do not comply with the demands.
The course of action you need to take (
if you really need to do this) is to buy some 11 speed Dura-Ace shifters, break them open remove the circuit board and mechanicals and then break open the st7971 and replace the appropriate parts.
This is not cost effective as you are breaking open two sets of shifters and if you make a mistake, its expensive way to learn what you did wrong.
Splicing wires from 10 speed Dura-Ace and introducing them into 11 speed Dura-Ace or Ultegra, is a sure fire way to put a smile on the face of those with the diagnostic equipment such as myself, who charge reasonable sums of money to tell you what you have sent up in smoke or damaged. It will not end well.
My advice would be to not mess around or hack 11 speed Dura-Ace unless you know what your doing, or am willing to accept that the learning curve can be expensive. I would personally advise sending the shifters back and buy the ST-9071 components.