Class A on a Ford F-53 chassis? I know E-350 is called a "one ton" and E-450 a "ton and a half" chassis. If F-53 is a "two-ton" then perhaps it is stiffer in frame and suspension. I've noticed some Class A's have a short wheelbase that would not be acceptable in a Class C. The specs for F-53 seem to allow for different tire sizes an capacities.
Class A used to be on a "truck" chassis meaning the front wheels were set closer together than the rears. Nowadays, it's an "RV" chassis with the front track closer to what the rear is. The E-Series of course has the narrower front track. Wide track on front axle is going to resist sway more than narrow. It's also a solid axle and that helps too.
A 37-ft Class A is big for a gas chassis.