So far I have not read anything that would stop me from towing a Escalade with the engine running. A friend tows one and he's on the third Remco pump that's failed while towing. Lack of this pump for X miles has not killed his tranny. Do you shift your Alison into neutral when stuck in traffic so the torque converter does not over heat it? Could idling in gear be the reason Caddy does not want it idle too long? Pretty sure a brake buddy has a gain control to adjust the amount of pressure put on the brake pedal. I agree having someone drive it would probably be easier than setting it up to tow once or twice a year.
In addition to the warnings below... the shorter the words the harder it is for me to understand it. NO being the hardest and and a little less difficult is CAN NOT. My Nissan Pathfinder can not be towed, but I DO. Back in the day when the front bumper was steel I towed many a car with the engine running.