How am I related? As I said, distantly...
I too am a descendant of Nicolas Cormier and his wife, Rosalie Hébert, through their son Nicolas (the brother of your ancestor Joseph Cormier).
As for relatives of your Cormiers, I know a Jeannine Brien from Woonsocket, RI whose mother (or grandmother?) was a Cormier from the same family (Mary, the sister of your Arthur), and is a closer cousin to you. If I see her or when I send her a Christmas card, I'll have her contact you via this message board or e-mail.
Best regards, Dennis