Had the same problem with mine.
The problem was the hub was too short for the shaft, so the prop didn't cover the splines (so when you put the washer and bolt on the non-'splined' part. This meant the washer didn't sit tight against the prop hub (therefore there was play in it)
Turned out I had missed out a spline washer, but you could just need a thicker one?
Might be talking crap, but if there is splines protruding from the the hub then the hub is too short and you need a second/thicker thrust washer.
Mine had quite a bit more play than 1mm though, about 3-4mm.
Excuse the poor explanation