Jerry,
Personally, I've never pulled a travel trailer with my H2 but manufacturers go to great lengths to "balance" travel trailers so that they pull well. All of those Jazz's have a tongue weight in the 700lb range. If you have rear air suspension, this shouldn't be a problem for you. If you get some electric brakes installed and have a good controller, IMO, you can pull these w/o much problem.
Of course, the H2 is specified from GM with a maximum GCWR of 14K lbs. and this is the number that determined the trailer weight rating. The ratings from GM does not take the air suspension into account. These numbers are the safe numbers GM published and, obviously, you can pull more than 6,800lbs w/o much trouble.
I would suggest getting a good brake controller installed and then going to the dealer and test pulling a few of the trailers to see what you are comfortable with.
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