I'm sticking my neck out on this one, the weight police are probably not going to like it.
The Draw-Tite hitch you line to is rated 12,000 pounds for weight distributing, 10,000 for weight carrying. With weight distribution, the hitch itself is good for a 11,000 trailer, since the rating is 12,000.
The highest "tow rating" I know of for an E-350 is 10,000 pounds, that would be the V-10 with 4.10 rear axle, which has 18,500 GCWR. The van with Powerstroke diesel (both the old 7.3 and the 6.0) both had high enough GCWR, at least 18,000 pounds, to give you 10,000 "tow rating."
Ford's "tow rating" for truck is more a guideline than it is a hard number. It is usually capped by either the hitch rating for Ford's tow package, or by the difference between GCWR and an estimated "curb weight" for the truck with standard equipment. It is an advertising number, and is sometimes called "maximum tow rating" because it can be really hard to find a truck equipped to meet the number.
The hard number is GCWR. Given an E-350 van loaded to 9500 pounds, an 18,500 GCWR leaves you only 9000 pounds for your tow. But an empty E-350 standard length commercial van weighs about 5900 pounds, so there is 12,100 of the GCWR left over for towing. Ford says 10,000 tow rating because Ford installs a 10,000 hitch on the van.
Curb weight is about 6000 for the extended E-350, 6500 for the 12 passenger van, 6900 for the extended 14/15 passenger van. With any of these, V-10 with 4.10 axle GCWR - Curb leaves at least 10,000 pounds, so Ford can still say "tow rating 10,000" based on their installation of a 10,000 pound hitch.
But you load up the van, it takes away from the tow rating. My E-350 passenger van has a GCWR of 13,000 and curb weight of 6300 for a "tow rating" of 6700. Does that mean I can tow a 6700 pound trailer? Only if the van is empty. I have a GVWR of 9500 pounds, for a cargo capacity of 3200 pounds. If I load the van to 9000 pounds (leaving something for hitch weight) my "tow rating" in that configuration is down to 4000 pounds.
Thus the "tow rating" is vague enough to have no legal meaning.
But pushing beyond GCWR for the van, that can be a problem. Is it dangerous? Not necessarily, if the trailer has adequate braking and the truck has adequate control. Sometimes GCWR is limited the drivetrain. The same van with 5.4 V8 has GCWR 5500 pounds less than the V-10 with 4.10 axle. The V-10 with 3.73 axle has GCWR 3500 pound less than the V-10 with 4.10 axle. They all have the same suspension components, weight carrying capacity, handling characteristics. All will handle the same with any given trailer, but the vans with smaller engines and lighter-duty transmissions will have less performance accelerating and climbing hills, and will wear out faster from the drivetrain overload.
Is it illegal to exceed a "tow rating" so ambiguously defined? It is not likely that you will find "tow rating" in any statutes or regulations. The relevant numbers are GVWR and GCWR. If you are paying road taxes based on those numbers, and you exceed them, then you have a weight violation. Not all states tax vehicles in this class by weight, but for those that do, it matters.
