I just went through some of the same issues with understanding how the numbers are calculated with my now old
RAM 1500. 1st..ignore that towing calculator (2nd link) as it has more flaws than I can count.
The hitch weight does not apply to the GCWR calculations. To determine if you are under GCWR you need to add the total weight of the TT and TV loaded. Using the published weights will cause you grief as no trailer or truck actually weighs what is published. I weighed my truck with nothing in it but me and a full tank of gas and the truck weighed 240 lbs more than published.
Where the hitch weight does get counted is on your payload or calculating the GVWR of the truck. To approximate that effect you will need to add the weight of all passengers (less 150 already accounted for the driver), all gear you plan on loading, trucks base weight plus the hitch weight. Be carefull on the hitch weight guess
.. you will want the hitch weight to equal appox 13% of the total weight of the trailer.
Try this link to see where I came out on my calculations. TV calculation help needed please
I realized that with the TT I was looking at, I could limit how I loaded it to stay on the ragged edge of limits but that wasn't an acceptable solution for me.