On one of the quilt shows on tv a long time ago, I heard a quilter say she was going to enter a quilt into competition and it would be judged for being square. she said to make hers work she laid it on the floor (undoubtedly waterproof) and spritzed water on it and shaped it. Said it was nearly sopping wet by the time she was satisfied. I wouldn't recommend this but......
Other quilters have used their husbands carpenter squares to assure the corners are straight.
My method is in construction....measuring as I go...constantly. If the borders are the measurements required, alter the top either by re stitching or easing or tugging to fit. It is possible to ease or stretch some... but big differences would have to be accounted for and adjustments made to the sashes or borders, small variances are not as noticeable in some instances there as in an outer edge. Then, pin, pin, pin, pin the premeasured sashes and/or borders to the quilt top and sew.
Hope this helps.
Now, if this is a competition quilt, I don't know what to do as I haven't any experience there.