Hey, so I talk to Lee, or 'behlinla', a Tech Advisor over on TCCA a lot and he helps me a ton on learning about things like this! So this wasn't all me!
He has some more to add to all of this after reading your posts. Why he doesn't just make an account.... I'm not sure! Here it is:
The AWD engagement is controlled by a active torque control coupling (ATCC) solenoid. The percentage of torque going to the rear wheels is directly proportional to the amount of current going through the ATCC solenoid, which is normally controlled by a PWM 12V signal generated by the AWD module. The AWD module communicates with the PCM over HS-CAN. Torque vectoring is directly proportional to throttle angle and any detected front wheel slip.
In theory, providing a constant 12V source to the solenoid via something like a simple switch would force full lockup, but the problem there would be the possibility of axle wind-up if you are driving on a paved surface. So I wouldn't think you want to have the axle at 100% for more than a few seconds. Not sure if there is still some slip in the unit at 100% solenoid duty cycle or not to prevent damage. Looking at scan data it looks like the module does run it at 100% for a few seconds.
The ideal solution would be an add-on box that provides the desired PWM signal to the solenoid that you could select. I'm guessing it's a high-current solenoid, so the control box would have to be rated to handle it. Perhaps something like those aftermarket turbo boost solenoid controllers would work.
Also not sure how the AWD module would react to having the solenoid being taken out of the circuit via a switch or having an external voltage applied, so that will probably cause trouble codes and possibly cause the PCM to enter a limp mode or limit torque in absence of a solenoid. Someone should unplug the solenoid and see what happens. You might be able to fool it with a resistor of the same value as the solenoid though. So when you flip the switch it puts the resistor in place of the solenoid and then sends full 12V to the solenoid. The other switch position puts it back to stock config.
Here's the diagram of the system on a 2011:
http://revbase.com/BBBMOTOR/Wd/DownloadPdf?id=875117