Sideway movement of the rear wheel

Yes, that is a solution I was thinking about. If you want to keep the same preload, then you have to put a small washer of the same thickness as all the hardened washers you are adding, between bolt 373 and axle 340. Then the spring built-in length will not change. You just have to make sure that bolt 373 is screwed far enough into axle 340. If it is too short, use a longer one.