Illegal / dangerous to pull 11,000 trailer rated 10,000 lbs?

You can install a heavier recevier and still be tow over 10,000 pounds and be under an specs.

The spec you need should follow is the Gross Combined Weight rating. As myself and others have mentioned, the advertised "tow rating" is limited by the original factory receiver. Ford publishes higher GCWRs for a reason. But if you don't want to do, then don't do it. If you're not comfortable with your setup, then you probably won't enjoy your trips.