I happen to descend from two of these people. I already had tentatively identified Gregory Belcher's wife as Katherine Alcock, however, this confirms it. One should note that their marriage record appears in both hers and his home parish (Aston, Warwickshirhe). I gained the maiden name of the wife of John Alcock as Elizabeth Wrightman and now my maternal grandparents are 10th cousins. They are also 9th cousins, once removed via the Burnham family.
Considering how close these Alcocks are to another group of Alcock emigrants, I'll surmise that they were cousins somehow and all from Warwickshire.