Agree with all of the above. You are doing a great job in understanding the numbers and I congratulate you for doing that.
I won't bother going through the math for you but you are good to go with your setup.
My rig is in my sig and works well. Your biggest concern is to make sure that you do not overload your truck bed to a point where your truck's payload capacity is exceeded.
You have slightly more payload than I do and I'm right at the limits with my SUV, family of 5 and the 233S. Its would be tempting to carry more in the bed if I had a pickup; that's why I mention it.
Again, you are asking all of the right questions in all of your threads before you buy. Your next post needs to be a hitch question