I was in contact with a gentleman a couple of months ago (sorry I don't remember his name) that has been in contact with Mayflower Society. Even though they recognize that Josiah Paine was a town clerk and historian of Harwich, actually wrote that "Nicholas and Constance had a daughter that was named for her mother who was the first wife of Daniel Doane of Eastham"...the Mayflower Society is still will not accept it. Bummer!
I have the Doane Family Book Vol 2 published in 1975. This is what is says:DANIEL DOANE: His marriages are not recorded in Eastham records. His 1st wife is believed by some genealogists to have been Constance Snow, dau. of Nicholas and Constance (Hopkins), but no documentary evidence has been found. The assumption is based upon the names of two of his children: Constant (a son) and Constance (a daughter). The Society of Mayflower Descendants has not accepted this assumption.