I know the door already closed on this issue, and my addition would certainly not qualify as 'new research since 1995', but Charles Edward Banks speaks to the question with some persuasion.
From Dr. Charles Edward Banks, The History of Martha's Vinyard, Vol I, pub. 1911, p 115:
"During that period he had married, about 1619, and family traditions and a record of some antiquity brings down to us the name of the bride of his youth as Abigail Parkus. [This is from a memorandum, genealogical in its character, prepared by Deacon William Mayhew, of Edgartown, who was born in 1748, and was thus within the sphere of close personal knowledge of his immediate ancestors. He was ten years old when Experience Mayhew, the great family exponent, died (1758), and Experience was about the same age when the old governor died, thus but one life spanned the gap between Thomas Senior and Deacon William. The memorandum was preserved by the Deacon's son, Thomas, and was in existence in 1854.] Further particularization has been given to this tradition by making her a daughter of that Parkhurst family, of which George Parkhurst of Watertown, Mass., 1643, was the first New England representative. George was the son of John Parkhurst of Ipswich, England, a clothier, and his sisters, Deborah and Elizabeth, came to this country with him, and were later residents of the Vineyard, the former as wife of John Smith and the latter of Joseph Merry. So far no documentary or recorded confirmation of his marriage has come to light, and some considerable search has been made to find the probable place where the marriage took place, but without avail. The tradition is given for what it is worth."