If I remember correctly, the Cooper A/T3 is also available in a LT 265/65/18. But if you have the 3.42 gearing, I would just go with the 275/65/18. That's what I did on our '10 Chevy 1500. Never noticed a difference in acceleration or anything regardless if towing or not. And the 275's were cheaper than the 265's by a fair amount!!!
I agree a LR E is not needed, but I would probably still go with a LT LR C. That's what I put on my '10 and was very happy with them towing ~7200lbs with ~920lbs tw.
The Cooper A/T3 have a mileage warranty even in a LT model. And performance is awesome with it!!! In all conditions (except mud- didn't venture off into that!) they performed very well in the 11k miles we had them. The reason for only 11k miles is we stepped up to our current 2500HD. Not sure what part of Canada your in, but in traveling to Northern Michigan and the Sault Ste Marie, Ont area for snowmobiling, I never second guessed the A/T3's. They performed beyond expectation!!! I will probably be putting a set on this fall to replace our factory pos SRA GY's. Still trying to decide for sure due to wanting to go to an ever so slightly bigger tire, but the selection is limited in a 20" rim...
My buddy has been very happy with the Toyo Open County AT2. They also have a mileage warranty in.
Good luck deciding!!!