Keep in mind that towing an Airstream doesn't need all that much power. I own a 34' International that weighs approx 7000lbs camp-ready.
Hp output, as measured at the wheel, at 60mph on the highway fluctuates from 40 to 60hp, depending on grade and wind. The highest output I've ever measured, accelerating from a standing start up a fairly steep grade was 148hp. Hp output was measured via the OBDII port.
My vehicle frequently goes into eco mode (switches two cylinders off) when on the highway.
A bigger truck will give you more payload, but I'd try and see what the H2 can do first.