Thank you Don for your hypothesis on the origin of our Sackfield line of Brewers. It is the first clue I ever saw to a family across the Atlantic.
Using your info, I have found one other site that gives the names of people of your first three generations--that of Janet Reakes from Australia that is easily found by searching Ancestry for Bartholomew Brewer. Janet does not name a Sackfield child and that is the key I need to fully accept your proposal.
Next, I think you may have an extra generation (and extra Sackfield). The Sackfield who died in James City county, VA, in 1699 (and had children Edmund and Katherine) was in Virginia nlt 1652. he was the only Brewer among 40 persons brought in by Jane Harmer so was in his late teens or early adulthood when he came over, most likely unmarried. His birth has been placed at 1632 but could have been several years earlier. Thus, he could have been your 4th generation Sackfield who named his two known children for his grandparents.