This might not work, but could you add a solid scalloped border around the striped border? The wavy lines of the scallops might make it harder to see that the striped border is not perfectly square? I agree with ckcowl's description of the longarming process, except that many longarmers float the top completely, not attaching it to any rollers. Another factor is that the quilted portion of the quilt is always a little smaller than the nonquilted portion, so keeping the lines straight is difficult. I struggle with keeping my quilts square and still have a lot to learn in that area. Renae Haddadin teaches a longarm class called "Hip to be Square" that I would like to take, and other professional longarmers have their own videos/methods/classes. In hindsight, since your outside border was striped, I wonder if would have helped to attach a temporary border, maybe muslin, around the quilt before giving it to the longarmer, with instructions that the muslin should not be quilted but was only there to give additional stability to the stripes, which did need to be aligned. It's just a thought, not sure that it would have made a difference in this case.