Are you loading the top on point? Or is the blocks in the quilt on point? Also, are the setting triangles outside edges on straight of grain or bias? If on bias that may be your problem as it sounds like you have stress on one side that is distorting when rolling.
If you are loading on point I can't help as I have yet to tackle this type, but if the blocks are what is on point I'll tell you how I load my quilts.
I usually mark the center of my quilts and have center marks on my leaders. I match these and either pin or baste stitch starting at that point and go to end, then start at center and go to other end. I have velcro on my poles which are also marked with center and when I load my quilt I match all center lines. At times I have to move one leader, but not by much--an inch or less..
I hope you have many suggestions and find one that works for you.