Having owned and shot a few Knick Single barrel traps over the years, I don't know what screw you are referring to as the "compensation screw" The screw that comes in from the front draws the forend wood snug to the forend iron. Unless the screw is loose and has been tightened, I don't know how one can tighten the fit, other than a small thin wood shim, or card as you have done. Those Ithaca guns were wonderful trap guns, and still are. They were an American Art Form, IMO.

Dennis Potter