A couple of comments and concerns.
It's a Z71. 4WD? If so changing gears will be very expensive because it's not just the rear axle that would get changed. Besides, that won't solve your issue. You need to get to the root of your problem.
Does your truck have a custom grill insert or shell? They look cool but can and do impede air flow. I have one on mine and didn't realize how it was affecting trans temps while towing until I towed in 90 degree heat around Indy last Sept. I was running close to 220. Once I realized what was going on I took the insert off and temps ran at 180. Air flow is critical.
Your trailer is most likely equipped with ST tires. They have a max speed rating of 65 mph. Running them at 70 is asking for a blowout. Something to keep in mind.
Dry weight it a fictional number. Dry weight it without options. As delivered it's at least 500# heavier than the listed dry weight. Now put your "stuff" in it. No one tows their trailer ready to camp at it's dry weight. It's very likely your trailer is 6000# ready to camp. But realistically even if you are towing at capacity, which is something like 7000# - 7500# for that truck, you still should not see trans temps that high.
Have you kept up with the maintenance? Fluid on a 4L60E should be changed every 50k miles with Dex VI.
Chuck D.
โAdventure is just bad planning.โ - Roald Amundsen
2013 Jayco X20E Hybrid
2016 Chevy Silverado Crew Cab Z71 LTZ2
2008 GMC Sierra SLE1 Crew Cab Z71 (traded)