really struggled keeping up with the 75mph.....
That's your biggest problem. You shouldn't be anywhere near that speed with a trailer in tow. Most trailer tires have a max speed rating of 65mph. Drag also increases exponentially with speed. It won't struggle nearly as much at 60mph and will save you a ton of gas.
You should definately have a trans cooler installed towing any full size trailer. I find it hard to believe that a dealer installed cooler could void their own warranty. I call BS on that.
Don't worry about it dropping into 3rd gear, won't hurt anything. It will tow better and cooler in 3rd at a higher rpm than it will bogging down in 4th. It does get tiring but won't hurt. I towed similar with my old '03 T4R which only had a 4speed. It was recommended to tow in 3rd with that trans. Same engine.