Most of those "rules" are hogwash since they're based on trailer size. Such advisories might hold true for sway controllers, but that's a whole different subject from weight distribution systems, many of which don't even perform that function.
Necessity for W/D is based strictly on the capacity of the tow vehicle to handle tongue weight. From your description it sounds to me like you've got plenty of payload, and that the rig will ride just about perfect once you're sittin' in the driver's seat. Give it a try without and see how things work. If you're concerned about sway potential, friction sway bars are an easy add on without all the hoo-haw of a w/d hitch.