My relentless pursuit to cure trailer sway - the dancing TT

You say you had to raise the rear of the truck about 3 inches to set the bars. It is normal to lift the rear to relieve enough weight/pressure to snap up the brackets. If doing that did bring the front of the truck back to unhitched height and the rear down 3/4 inch it sounds like you are close. 3 links loose sounds like 5 or 6 under load which is good too.