Run in 4th with ECT PWR on. 4th gear is 1:1 and it's less wear on the torque converter as it's not locking and unlocking. The MPG difference when towing is marginal between 4th and 5th. The engine will hum along at 3,000 rpms all day. And it's minimal engine wear in 4th but much more transmission wear in 5th. (Side note: I've done a Blackstone analysis with TBN after 6500 miles, 4000 of which were towing including a trip out to Teluride and back and even running in 4th the whole time they said my oil had plenty of additives still in it and looked good so "run 8000 miles next time and send us a sample". A nearly 8 quart oil pan probably helps.)
If you're really concerned add a larger or additional transmission cooler pre-radiator. Do it pre-radiator because you want the fluid to get up to operating temp (~195F) and doing so ensures if it "overcools" the radiator will warm it correctly. If you do it post-radiator you may run with fluid that's too cold, particularly if you're on the highway when temps are in the 40s or 50s, which provides *less* lubrication.
BTW yes Toyota says you can run in 5th, but as you've seen the transmission temps will be higher. That said if you downshift from 6th to 5th on the highway when you're not towing you'll see your temps will creep up as well. Really I just avoid 5th gear for any extended amount of time...