The Register of the Society of Colonial Wars establishes Ezekiel as the father of Freeland Gardner, and we have evidence that William and Eliza were Freeland's siblings.
Family search has a record of a Sally Savage marrying an Ezekiel Gardner. (This Ezekiel was born around 1770, which does not exactly match the Find a Grave date for the Fort Ann Ezekiel). The online resource Family of John Savage, Middletown Conn., by James Francis Savage, has an entry for William Savage b 18 Sep 1699 m Sarah Savage. Their firstborn was William b 19 Feb 1727 m Martha Gibson. The children of William and Martha included Sally. The text goes on to say, "This family removed from Middletown to Sandisfield (?) Mass, and thence to eastern New York, where descendants now dwell..." https://ia800209.us.archive.org/11/items/FamilyOfJohnSavageOfMiddletownConn/savage.pdf
Sally Savage is at Wiki with #4986, born about 1781.
I have two DNA matches with the William Savage/Sarah Savage couple.
The Door County (WI) Historical Society confirmed that Freeland B. Gardner's parents were Ezekiel Gardiner and Sally Savage, and that Freeland had a brother William. But I don't know what sources they are relying on.
As a preliminary guess based on the family trees of DNA matches, Ezekiel's grandparents might have been George Gardiner-1558 and Sarah Boss. This is my reasoning:
I have at least two matches with George Gardiner-378 and Susannah Hazard. These would be Ezekiel's hypothetical great grandparents. George and Susannah had three sons: George Jr, Ezekiel, and Nicholas. One of these could be the Fort Ann Ezekiel's grandfather. I rule out Ezekiel, because he was the father of Ezekiel M. of Lorraine, NY, not Fort Ann. Nicholas, who married Hannah Champlin, is a possibility, but I like George Jr. even better, because his wife Sarah Boss has Phillip Sherman/Sarah Odding in her tree, a couple that I see many times. Sarah Boss's mother was also a Gardiner, granddaughter of Benoni Gardner, who also shows up several times. On the minus side, I have no legitimate matches with surname Boss, but the Bosses were fairly recent immigrants from Holland.
Assuming George Gardiner and Sarah Boss were Ezekiel's grandparents, I consider their sons, George III, Rufus, William, and Levi as candidates for Ezekiel's father. I don't have wives' names for George III, Rufus, or Levi, but William, b. 8 Sep 1749, married Mary Boone-3789. Mary has the couple George Wightman and Elizabeth Updyke in her tree, and I have matches with this couple. I also have a good number of matches with Bentley and Sweet, also names in her tree. I have a number of matches with Boone, but unfortunately those are mostly of a different line (the Daniel Boone line).
Another reason I prefer William Gardiner-2957 and Mary Boone as parents for the Fort Ann Ezekiel is that my ancestor, presumably Ezekiel's son, is named William. The names George, Rufus, and Levi don't show up in later generations as far as I know (although my ancestor might have had brothers that I don't know about).
Have you taken a DNA test? If so, login to add it. If not, see our friends at Ancestry DNA.
Ezekiel is 22 degrees from Herbert Adair, 19 degrees from Richard Adams, 19 degrees from Mel Blanc, 23 degrees from Dick Bruna, 21 degrees from Bunny DeBarge, 30 degrees from Peter Dinklage, 19 degrees from Sam Edwards, 17 degrees from Ginnifer Goodwin, 21 degrees from Marty Krofft, 15 degrees from Junius Matthews, 15 degrees from Rachel Mellon and 20 degrees from Harold Warstler on our single family tree. Login to find your connection.