Sandy, Your email still is not getting through so I'll post the answer here.
I have heard of another line of Adam's coming into NJ from Ireland.I haven't been working on this family for a long time and have very little on the Adams'. The decendants of the New England family lived in Port Republic, they had a son named Mark but they are not the family of the Mark I am seeking. Funny you should ask about John W's middle initial.Recently, I have received several requests for the same. It is not on his marriage records or pension papers or tombstone. I will save your email and when I actively pursue this family, and if I find it I will let you know.
Sandy from NJ BTW, his father may have been one of the William Adams.