The GM owners manual probably says trans tow/haul mode is not necessary unless you are towing at 80% of GCWR. However, my opinion is that towing any high walled trailer is more work than any low walled trailer and one should use tow/haul mode. Weight when towing a high walled RV at 55mph+ doesn't matter because the amount of work needed is due to pulling two sheets of plywood through the air.
6th gear is not locked out in tow/haul mode. It is just not likely to shift into it under 65mph, maybe 70mph for your 3.42 axle. My 6.0/3.73 will shift into 6th gear around 65mph in tow/haul mode.
The torque converter will lock in all but first gear in both regualr and tow.haul modes. The trans has to unlock the torque converter every time it shifts gears. Unlocked TC is what drives the trans temp up, so it is wise to keep it locked as best you can.
I use tow/haul mode and M5 and tow at 65-70mph most of the time. That's 2200-2400rpm. 2500rpm in 4th seems just right for your conditions. Usually enough power, TC locked, and good throttle response. That's what I recommend for you, tow/haul and M4.
