Yes, this research is very exciting.When I started my genealogy search, all I had was the names of my paternal grandparents.Now I have gone back into the mid to late 1500's, but I'm at a road-block in Lesum, a village just north of Bremen.
With a lot of help in Bremen, I've learned that the oldest ancestor of the Mayor's Branch was Berent Heineken.He was first documented as taking the Citizen's Oath for Bremen in 1624, and it was noted then that he came from Lesum.
Officially, he is confirmed to be my oldest ancestor and 7th great-grandfather, however, a 1586 Lesum tax register listed another Berent Heineken.And as my confirmed ancestor died in Bremen in 1668, I don't think it was the same person.But for obvious reasons, I do think that they're related.
There was a small window in which the Heinekens inhabited Lesum.I know that they lived there briefly and where they went, but I don't know the identity of the 1586 Berent Heineken nor where he came from since the records don't show anything in Lesum before the 1586 record.
Because of slight variations in surnames, I can only assume that my ancestors were known by another name and came from some other location.It's possible that the individuals you mentioned in your research, Heinickens, Heinick, Heincke, Henigk and Henke, along with the various movements, might indicate a common ancestor.