I already correspond with Jesse Haye (from Belgium) and we have shared information on the Haye family.
From 1671 we cannot find a common ancestor and we believe that the answer will be found in the Berne region.
As I said the first ancestor of my line I can find is Johan Hajen, born in 1671 in Wehrderhöhle.
He married Hille Scriver.
Jesse's first ancestor is also from the same area and named Heinrich 'Le Dirk' Haye (or Hajen).
He was born in 1675 (If I remember well enough).
They may or may not be related, we believe they are but we do not know how.
As it stands we have come to a halt and hope that some of our German friends may have already researched their ancestors and found links to the Haye or Hajen family, or even better have researched the Haye family.
There are Haye's in Butjadingen, in Berne ( a farm owned by a lady who was born a Haye).
We hope that something might come through the mail.
Best wishes and thanks for your speedy reply.