Any picture of the (damaged) nock? I've worked with yew a fair number of times, but never had a string 'bite' into the nock. If the wood is really damaged from only bracing the bow a few times, it would get worse over time. Is the wood really THAT soft? Is the string very thin?
A picture will definately help in determining how to solve the problem. A nockoverlay will certainly help, but if you don't like an overlay, we might come up with a better solution such as wrapping serving around the string loop. Try to take a picture of the nock in broad daylight, outdoors, with the camera set on macro mode (probably the icon with a little flower).