Isaac Leet (1646-1686) ancestry

Isaac Leet's ancestry has been a tough nut.  Michael Leet, in "The Family Face" speculates that Isaac's father is Gregory Leete of Badby, Northamptonshire.  But extant information can't link Gregory to the primary Leete lines in Cambridgeshire.  (I do understand that boundaries and names of places change.  If you look at the English map, Badby isn't very far from a number of towns that have confirmed recorded Leetes.)

One thing for sure:  all the entries in the genealogy databases and trees that link him directly to Gov William Leete and his father are very wrong!

There is one very speculative possibility, based on the Isaac Leete family tradition.  That is that Isaac is the son of "the other" William Leete.  In the 1613 Visitation, John of Dodington recorded his son, William, who was "half a year and more" of age.  (By the way, it is reasonable to suggest that Gov William Leete was born in 1612.  In fact, Michael Leete, in his records, does just that!)  Now this John was the son of Thomas Leete and his second wife, Dorothy Warde.  But the Visitation mentions another son of Thomas also name John.  This 2nd John's mother was Thomas's 3rd wife, Maria Slade.  He was born in 1575, whereas the first John was born in 1570.  He is called "John of Islington"

John of Islington had a son, William, born 5 Aug 1613.  And there lies the confusion in the published genealogical records.  Two Johns with the same father but different mothers and two Williams with essentially the same birthday.  William Leete definitely existed:  somewhere in the Family Face Michael mentions a gravestone with that date in Oakington.  

I'm working on this second William, reading and rereading Michael Leete's discussion.  Any help? I'm just wondering, given the Isaac Leete family oral tradition, could it be possible that Isaac's father was this second William?  The birth dates of father and son are right.