In your scenario the only advantage the gas truck will have is price. ALL other factors favor diesel. With that in mind you may save a few $$ with the gasser. Some of the savings will be spent on fuel.
The rest of your savings will go towards putting up with the deficiencies of towing with a gas engines. You can pay in cash for the diesel or you can pay in patience with the gasser.
Don't get me wrong there is a place in the towing world for a gasser, however it is not on a year long cross country trip. There just isn't enough savings to make the gasser worthwhile.