Thank you for your detailed and informative response! I went back to Gedmatch as you suggested and ran the Chromosome Segment Comparison utility on my kit specifically for positions between 69,788,586 and 70,017,488 on chromosome 3. My grandfather's kit didn't show up, but my grandmother certainly did (she was a nearly perfect match) so you are right on the money!
I had my sister's DNA tested with Ancestry.com but will need to wait until Gedmatch accepts uploads again before I run the utility on her kit.
I knew my grandma's mother, first cousins, her only brother, her brother's family, and her aunts and uncles, and not a single one of them exhibited signs of the syndrome. I wonder what happened to cause the mutation to show up with my grandma's children. My mother's oldest brother was mentally challenged - I wonder if that has anything to do with this.
Thanks again. I will look into consulting a genetic counselor! This all is so interesting.