No damage to chamber.
This is a normal occurance with Less than full lenght sized brass after several firings at max allowable pressures/loadings. Also, depending on seating depth, you may be finishing the seating process if you are attempting to seat to the groove depth.
Try this;
Turn in the sizer die till you are just touching the shoulder (there are different methods of this, but I prefer to see light burnishing marks on the shoulders where they are contacting the die). Then turn approx 1/4-1/3 additional turn in on the die. This will ever so slightly set back the shoulder so that the ammo will still seat with minimal force.
With the steep angle of the WSSM, you will still get minimal case stretching/growth and ease of feeding. You only really need to minimize the headspacing to get the benifits of not setting back the neck. Following the above technique I still get many loadings out of my .300 RUM. I've fired some cases as many a 7 times, and cases are still under the max OAL before trimming. You should get similar results from the WSSM.