Back in the old days I followed advice put out by one of the early writers on making bows. He recommended leaving and island of wood over pins.
After having a few "islands" fail I now follow the same grain I choose for a bows back over the pins.
I usually use a Dremel with a steel burr to do my initial ring chasing over pins. As soon as I break through to the correct grain in most of the areas around the pin I switch to my pin knot scraper or a curved end cabinet scraper to finish the job.
Here is a pin knot scraper I made out of a concrete nail, really good for fine work around pins.