Rear tire rubs around corners

I've had 5 wagons. All had OEM size or near OEM size tires. I've never had any issues with tires rubbing. Side to side rear axle movement never crossed my mind. My most recent acquisition is a 94 Caprice wagon. It came with 20X9 rims. The tires on it are 275/40/20. I can just get my fingers between the tire and the skirt on the drivers side. On the passenger side, I cannot get my fingers between the fender skirt and the tire. When making a right turn at anything faster than idle, the rear pass. tire rubs the skirt. Would boxed lower control arms lessen the side to side axle movement? Would I need to upgrade the upper control arms too? On all my previous wagons, I installed UMI boxed lower control arms. The '94 is still stock. I haven't done it to this one yet. Will that help? Do I need the uppers too. Or am I barking up the wrong tree altogether?

The uppers control side to side motion. Lowers only control front to back. Urethane upper bushings would probably solve the rubbing. You should also center the body on the frame.