The barn doors went away on by 2004, maybe 2005 on the GM full sized SUVs. So If you want something later, then you have to get the hatch. On the 2007-2014 generation, the rear door has two opening options. Glass only or full rear hatch door. I cannot speak for the 2000-2006 or 2015+ models. My 2011 model can open either method with my TT attached.
It is true that there is one model 2000+ 2500 that has a lower tow rating than the Denali Yukon 6.2L. That is the 2000-2006 6.0L/3.73 axle. The 6.0L/4.10 and 8.1L with either axle have higher tow rating than any half ton SUV. Since you mentioned 6.2L (2007+ model GMC Yukon Denali Only) and are discussing tow ratings, keep in mind that towing a travel trailer at any of these ratings will likely exceed at least one other of all these vehicle's ratings. If you like Denali level of equipment and have a larger family, then payload will be a problem.
Can you narrow down the years in which you are interested?
I'll put a plug in now for the 2008-2013 Suburban 2500 and Yukon XL 2500. They are kind of rare, but every one has the necessary towing equipment standard. It should handle most 8000 pound loaded TTs with at least 2000 pounds of payload and 1000 pound TW limit. The powertrain is rock very reliable and gets decent fuell economy for it's size. We love our 2011!