I think your going to find that most class c on E-350 and E-450 are rated to tow a max of 5000 lbs. Most of the class 3 hitches are rated at 5000 lbs. Next jump would be a class 4 or a class 5 hitch.
I recently replaced the cheapo class 3 hitch on my class c. Replaced it with a class 5, just for the superior strength.
But, I tow a 3100 lb Subaru. My class c is a 2012 Forrest River Lexington with a V-10. It's adaquate for up to 5000 lbs. No way would I consider towing 7500 lbs. Putting way to much on the engine/tranny. To safely tow what you want (notice the key word--safely) your going to be looking at a super c, most of which are rated to tow upwards of 10,000 lbs. But, their not small, beginning at around 34 ft, and on diesel chassis.
Grumpy