I spent all of my summers in Mira Gut, Cape Breton. The house next to us was owned by a Lingan Tutty. The property was in his family for many generations. The reason that I am mentioning this to you is there is a Cemetery in Mira Gut along the road on the ocean that has a number of Tuttys buried there. If your able to find someone in the area to take a look something might turn up.
I would offer but I am currently in Ontario. Next time I'm home to visit (next summer) I'll be sure to take a look.