Umm - if everything is cut, sewn, and pressed correctly, why is it necessary to do a major "squaring up" of anything at the end?
Before adding borders, I do measure the body of the quilt (both directions) and then use the average measurement for the borders. I will ease the edge pieces (the row before the border) as necessary. I mark the border strip at appropriate intervals to help with the matching.
That said, after putting the top on top of the backing, I do check it to make sure that I placed it correctly. I use a 16 1/2 inch square on the corners and then run yardsticks along the edges to make sure that it is laying straight.