Do you have the X2 mount or the original mount on the PS2? That smaller adapter is for the X2 mount when pulling on the top mount head. The original mount does not need that piece. It is not for the throat pull. for the I would suggest you stop doing throat pulls once I got the butt cap pull adapter. It's a much easier stringing process from the cap than the throat. Pro Stringer has instructions on this:
Regarding string damage on tension head, other than the normal bending of the string, I've strung natural gut, even the cheap V5 ones and never had a scuff. We use round polys and still string with the PS2.0 on the road. My kids have not complained about string scuffing. I suggest you contact Pro Stringer regarding this issue. Perhaps
@James_PS can help out.