This almost sounds like the batting wasn't loaded square to begin with. Was this a prepackaged bat or cut from a roll? If cut from a roll the cut may not have been straight, if prepackaged it may have been wonky on the end you lined up with your top. Or a wrinkle in the batting may have gotten quilted in. Unfortunately I am not familiar with this frame so i can't offer any ideas for a solution. You may be able to work in a wedge of batting if it continues to go so off kilter you won't have any batting in one side as you progress. The quilting should hold it in place .
As far as your backing being loose on the sides that is also an indication the backing was out of square when loading. Do you have any way to attach side clamps to this frame? This may help hold the back a bit tauter for you.