4000 pounds loaded for what you have should be fine. That's well under your tow rating. Using the first 4 gears only should provide decent performance and improved fuel economy (Tow Haul, M4). Get a trans cooler. $50, or $200 installed. Towing in the 2500rpm range (whatever gear that is) should provide a decent towing experience. Better throttle response, fewer downshifts, lower trans temps, and better fuel economy.
Read this thread of similar circumstances.
If you want to change the TV, then:
2008+ 2500 Suburban/Yukon XL
00-06 2500 Suburban/Yukon XL
00-05 Excursion
Do it right. Check the payload stickers as you shop. I don't like the Titan/Armada gearing. And it doesn't have that much power like the Hemi to make up for its poor gearing. Very few gas engines can tow any high walled RV in top gear at 65mph.