well, my eyes are on the floor after hours of followup researching, and I want to let you know that it's looking very good.The R.M. Hay you all managed to dig up does appear to be my Hay, which is miraculous.
I want to chase things a little further before I say Yes, this is it, but it's looking very positive from here at the moment.
I'm working hard on William, M.D.'s later life here in the U.S., I've contacted some local historical societies in the U.S. towns where he was practicing to try to figure out his movements and where he might be interred, or if he went home to Canada in older age/retirement.I also found another little U.S. article about him which corroborates the connections to his parents R.M. and Charlotte.
I'm sorry Charlotte died relatively early.You get really attached to these people in the course of researching them, and sad when you lose them.I love her name, Charlotte.