You understand the numbers, and yours are correct. IMO, even though I am not, many people towing FWs exceed the GVWR of the tow vehicle. I have no problem with this on a 3/4 ton truck, within reason, say 500 lbs or less. The important number is the RAWR, or tire max load.
In your case, I would not be worried about adding 2,200 lbs of pin wt, plus a 200 lb hitch, as long as you don't add any additional heavy items to the bed. This will put you over GVWR, but well under rear axle and tire rating.
Jerry