If the weight of the vehicle is not on the wheels then locking diffs or snow tires won't help. If you are high centered you are high centered and you have to solve that problem first.
Typically, when you go off the road with some speed you will be high on the front but less so on the back. In this case we couldn't really tell as the rear wheels were not turning (AWD likely defaults to FWD for most driving conditions). In these cases I don't like digging around too much for fear that the car will settle/shift onto someone. We grabbed at the front bumper tow point, rotating the car 45* counterclockwise. At some point during this the rear axel decided to start helping and it half drove itself back onto the road.