The Rear GAWR may be close. If you can run it over the scale empty to see what your unloaded Rear axle is, then you will get an idea of what it has left for your tongue weight etc.
The payload is 1631 minus your weight over the 150 lbs they allow in that number, the weight of your DW and children/dog, and WD hitch shank equals what you will have available for tongue weight....could be close.
Again, the scales will tell the whole story.
You're right, they won't like it, but it lets them know that you want them to prove that your truck is capable.
Not sure about the tire rating number you have there. The tires should be stamped with a Max Load rating on them in pounds.
