Newbie and can't figure out the "What can I tow" math

So I probably need to find a trailer closer to 6000 GVWR then to be safe?

6000 x .13 = 780 lbs tongue weight.
780 + 80 (wd hitch) = 860 lbs
1588-860 = 728 lbs.
Currently the weight of my family is ~610. Even then there isn't much wiggle room for growth with 3 boys ages 8, 11, 14.

But if I am understanding this properly, at least I have a better feel for what I should be looking for.

Is this an unusual way of doing the math? Shouldn't trailer GVWR be a searching option then?