You will discover that if you stay under the GVWR, in most cases you will be under all other ratings. Your calculations agree. Not sure why you are calling me out on something that is so obvious. Then you turn around and prove my point with your example. (Though it gets a little obscure):
"My best way to figure max tow rating, is gvwr less the loaded wt of the rig gives max payload for hw. Take this number, divide by the hw % one needs, you then have the max trailer you can tow. If you have 1000 lbs for hw, you have a max trailer of 10K at 10%, if 20% is needed, your max trailer is 5000 lbs. Tow ratings etc be danged."