Do they make their own corned beef like the deli's up north? We have yet to find a good corned beef sandwich on the island that doesn't use pre-cooked meat like lunch meat

They may, the kitchen is more a galley type similar of a small diner. We had breafast there, my impression of the food we were served is it all was made on the premises.

Gruby's deli on Hilton Head Island is very similar to the places in New York. However, not sure if they cook corn beef in their kitchen. Some of the BBQ places have brisket prepared on their establishments.