I don't know of ANY of the major manufacturers who make an all season tire in an LT load range that would NOT be suitable for towing. I'd look at service instead. I've had great luck with Cooper Discover LT tires, as they are quiet, have good traction and a great ride. Problem is they do not have any nationwide warranty so if you have an issue come up while traveling you pay for the replacement tire and are reimbursed by the dealer where you purchased the tire. They are not the ONLY company who present this problem. Ask about nationwide road hazard to avoid issues like this.
Good luck / Skip