It could be the other wheel bearing. Bearings have inner and outer races, so loading on left turns could still be the left wheel bearing, it happened to me. Now my bearing was grinding on left turns and straight ahead. When I removed it had a small amount of play yet the inside balls and races looked really smooth. It did not appear to be worn but it was loose.
If you are thinking tires, could you put the left on the right and right on the left and see if it changes anything?
