I agree about the dry weight fibbing by manufacturers, but that's a little harsh on the towing capabilities of current generation MDX or Pilot. I used to tow a roughly 3500-4000 pound boat and trailer in moderately hilly terrain with multiple generations of MDX and Pilot without major problems. And I once towed a 6'x12' U-Haul trailer across a couple states with our 2014 MDX. That trailer weighs 2000 pounds empty, and it wasn't empty.
One issue with travel trailers will be the frontal area that sticks out above the roofline of the MDX. That creates a constant aerodynamic drag. And long travel trailers may have issues with sway because of the relatively soft suspension of MDX compared to a big honkin diesel truck. Both issues can be mitigated by just slowing down.
As for weight, Acura says to deduct 200 pounds from maximum tow weight for every 1000 feet of elevation. That's about 1200 pounds for you, CO, so even with the ATF cooler, now you're at 3800 pounds capacity. And without the cooler, it would be 2300 pounds. You're also supposed to deduct the weight of cargo in the vehicle, and "excess" passengers ( more than one in addition to driver ). So it's not really very hard to bump up against the limits of what's "recommended". But unlike some manufacturers, Honda/Acura does actually test their vehicles to ensure they can handle the rated tow weight.
If you're willing to slow down and enjoy the scenery, and you're willing to pack light, it may be fine. If it's going to be a routine thing, a pop-up trailer might be a better bet.