You already said the TT weighs more than the tow rating of such vehicle. Seems like GM thinks it is not the right vehicle for your situation.
A 10k pound TT will have about 1300 pounds of TW. That's 300 pounds more than the receiver is rated for. There are no aftermarket receivers that fit since GM built it into the frame of every one they built.
1300 pounds of TW with about 1400 pounds of payload available. I find it hard to believe that everyone planning to travel inside the SUV will weight under 100 pounds combined.
The last SUV that is capable of towing a 10k pound loaded TT was built in 2006. If you went to a pickup, then I cannot recommend and half ton. Even the HD payload F-150 doesn't have a receiver capable of 1300 pounds of TW. That's solidly into 3/4+ ton vehicles. The GM 1-ton van is even a little weak on powertrain for 10k loaded.