Up front, my upholstery experience has been installing pre made covers. No sewing experience so take my thoughts with a grain of salt. Looking at the stretch pattern, I am thinking what do I need to do to eliminate them and correct the location of the right hand (left in pic) to make a perfect line across. First, I would loosen the top and tighten the bottom to pull the button line down. It appears to me the sides and bottom were affixed and then the top was pulled to firm every thing up and in doing so, the button row moved up from the semi relaxed position. Since the bottom and sides could move very little, the puckers developed a downward tilt on the two side buttons and the increased upward movement effectively tightened the buttons, pulling them further thus creating the puckers between the buttons. My fix would be to locate the button placements and pull the longer than needed threads through the affixed padding. Next, I would pull the cover until the sides and front were straight and even, button row straight. The last thing I would do would be to pull the button tension incrementally until I got the desired depth. These should be straight pulls thus even tension on the cover.