The problem with towing in OD with an automatic is that the engine RPM is to low, thus the pump speed is too low and not enough transmission fluid is circulated around the transmission to keep it cool under a towing load. A transmission cooler should help, but I would still follow the manufactures recommendations.
It has been a few years, so the details are fuzzy, but I do know that older GM trucks (80s and early 90s with 700R4 and 4L60) had I think a 7 vane transmission pump which was poor at the best of times. The newer transmissions have a 13 vane pump (4L60E?) which improves performance at lower RPM.
To get around all of these problems, buy a truck with a stick shift.