There are many factors that determine a vehicles ability and limits for towing. Horsepower is just one small detail. The OP is referencing his current coach, a 1997 Tioga. I had a 1992 Tioga Arrow. There of the chassis was extended with bolt on frame extensions. Possibly the 97 is the same way. The 1992 was limited to 3,500 pounds despite the 5,000 pound hitch. The motorhome had some damage from towing. You knew it walking inside. It was obvious where the frame extensions began from the crease and tilt in the floor.
Flat towing 4 wheels down especially larger, heavier vehicles is much more stressful than just the weight. With the long overhang behind the rear axle the side forces can be brutal. Light vehicles with small tires are forgiving as the front tires can slide and scrub as needed. Front heavy vehicles something has to get stressed. Usually, the towing component and the frame, suspension of both vehicles. Looking for a class C for towing, look for longer wheelbases on shorter rigs and watch that the chassis frame makes it to the hitch. For the E-350, E450, the weak component is the rear axle. Good lubes, changed often.