I also did Beartooth in September 2012 on the amazing 11K altitude and towing behind my 3.6R 1800 lbs camper from Cooke City to Red Lodge.
It was a comfortable and not very fast driving. I sometimes selected gears manually on some very steep sections.
The power of 3.6R was adequate for towing my camper.
I was worrying about this highway (extraordinarily beautiful road by the way) as I read somewhere that the normally aspirated engine looses about 3% of its power for each 1000 ft of elevation. But driving with towing was OK and not particularly stressful for both the car and the driver

some pictures from Beartooth:
http://goo.gl/83Kkl