Thomas Winslow's marriage record is found in the Supplement (p 6) to Vol I of Hinshaw's Encyclopedia of American Quaker Genealogy. In my second edition hardbound copy of Hinshaw the supplement is actually bound with Vol I. It reads, "1704, 9, 2. Thomas, s Timothy, Perquimans; m Elizabeth Clare." Unless there is some error in the transcription resulting in a mis-identification of his father, then his father is Timothy Winslow, not Joseph Winslow of the Great Migration.
Hinshaw notes that the supplement comes from 80 manuscript pages of Perquimans MM records found in a second-hand bookshop near Glens Falls, New York. This was found after 1936 (first publication) and before 1948 (second edition) so this information was not known to Ellen Goode Winslow whose book which touches on the topic of Thomas' father was published in 1931.
Edit: Bobbie, I first wrote here that we could safely detach however I want to see if I can find an image of the original manuscript to make sure there isn't mis-identification of his father since the father of his wife is a Timothy.