Thanks for this idea, it was definitely worth trying.
The power was cut on the + side, and after bypassing the circuit and trying the new hacked battery, the camera does receive power and seems to communicate with the battery. Unfortunately, despite receiving a good voltage (~8.2 V) the camera acts as if the battery is flat and does not turn on, showing only a flashing empty battery on the LCD display. Presumably, the battery circuitry tells the camera that the battery is flat, as it hasn't registered any power going into the battery.
This workaround doesn't solve my problem then, but for the sake of curiosity, I tried the trick of putting the dummy battery to charge for a while (connected to the big external battery). This indeed makes the camera work and reports that the battery is not empty. So the problem is that if the battery doesn't communicate, the camera requires that annoying manual approval to use the battery, and if it does communicate, it will obey what the battery circuitry says about battery power, which has nothing to do with the actual power in the external battery.
Is it within the possibilities of ML to disable that battery approval check?
Thanks!