Your truck has a 5.3L engine, not a 5.7L engine. I mention that so you will have better luck searching for the aftermarket modification to defeat the AFM feature. It can be done and it should solve your problem without trading trucks.
Chevy ONLY put this system on the 5.3L engine. None of the other truck engines have it so you don't need to necessarily avoid a Chevy truck if you choose to trade away from this engine instead of modifying it.
No "1/2 ton" truck can tow a 13,000 pound RV because you won't have enough payload to support the likely 2,000 pounds of tongue weight plus the WDH, passengers, and stuff. If you were towing a 13,000 pound boat or a flatbed load of bricks with a lower percentage of tongue weight than an RV then I see no trouble using a truck at it's rated tow capacity.