Looking at the Great Migration database at NEHGS, there was a Zachariah who would have been born in 1595 give or take. He had a wife Sarah. This Zachariah arrived in 1635 on the Truelove. I found no trace of an Abijah or Peter. Also, there wasn't any Whitman listed as dying in 1623 in Massachusetts Bay..
Also, ALL of the Ancestry source links are broken so can't be examined. I think a lot more work needs to be done.