Here's the bit about the direct line up from the emigrant Edward:
Clarence Almon Torrey, “English Origin of Edward1 Gilman,” in The American Genealogist, 11 (1934): 137-138.
Edward1 Gilman, who came from Hingham, England, in 1638, and settled at Hingham, Massachusetts, was not a son of Robert and Mary (-----) Gilman, as stated by Arthur Gilman in his Gilman Genealogy. Robert Giman, who was baptized July 10, 1559, at Caston, co. Norfolk, England, had a brother Edward, baptized there Apr. 20, 1557. This Edward was the father of Edward Gilman, the emigrant of 1638. Credit for this discovery is due to the late Col. Charles Edward Banks, who found a deposition of the younger Edward, made in 1637, when, according to the record, he was fifty years of age. He mentioned his father Edward in the deposition.
The corrected Gilman line is as follows:
# Edward Gilman m June 21, 1550, Rose Rysse
# Edward Gilman, bapt Apr 20, 1557; m. _____ _____.
# Edward Gilman, the emigrant, b circa 1587 [age 50 in 1637]; d. at Exeter, N.H.; m. at Hingham, England, June 3, 1614, Mary Clark
… Edward, baptized in 1557… inherited a house and land in Halwicks, in accordance with his father’s will. The location of this property has not been ascertained. He probably lived at Hingham, England, for a few years subsequent to 1600. Hingham parish records, which being in 1600, mention two daughters:
# Margaret, bapt. Aug. 1, 1602
# Sarah, bapt. Dec. 4, 1603.* [*This date is stated as Oct. 4 or as Dec. 4 in different copies of the Hngham records. The latter date seems the more likely, from the position of the entry in relation to dates of adjacent entries.]
No further record concerning these daughters and their father are found in the parish register.