I bet the basement in our 5er would come close. 8' from one side to the other, approx 5' for to aft, but not quite as high, but there is still storage in the forward compartment and in the bed of the TV in front of the hitch.
I agree an Air Stream should tow better than another TT, but I would have to see proof that it would tow better than a 5er. While granted it would track better, but the feature that allows it to track better is the same thing that can allow it to sway.
My opinions only, having never towed an Air Stream.
