There are/were lots of discussions about the rear slide plate some time ago. On larger machines, setscrews through the slide plate are a common means of adjustment - on these relatively small machines, adding a filler piece is a better fix. When you get the slop down to a reasonable amount, you'll probably find you need to refine the surface on the underside of the bed.
IIRC, there were some folks who added the old bed to the longer one, with everything mounted on a rigid base.
Roy
