BeerCan,
You have something else like shocks, alignment, worn steering and suspension joints, etc that's causing your "square tire" feeling. An out of round tire shows it's defect simply by spinning on or off the vehicle and also shows if it's unbalanced beyond spec. I seriously doubt your problem is tire related as even you stated the suspect tires were replaced.
We're well over a dozen LTX Michelin 4 tire sets on our larger SUV vehicles/pickups over the last 11 years alone including my businesses pickups and only one tire has ever been out of spec and was replaced before it was put on. Never had any tire vibrations or "square" type feelings on any of them. Last LTX 265/75/16 M+S2 "E" tires were put on November 2012 and are as smooth as can be just like the others and their traction and treadwear is superb just like the independent rating tests have all revealed.