I'm afraid the Siward link has problems due to his male line dying out, allied to some date discrepancies. The actual truth as we know it is fascinating, though. I'll PM some info.
Re some who link to your descendants:
Robert (4th of 11) Bapt 16 Jul 1785 at Hindley Steel Farm - died 12 Sep 1866 at Swalwell, Whickham
His father was John (youngest of 5) Bapt 12 Apr 1749, born Butterburn Farm, Cumbria, died 2 Apr 1829 at Hindley Steel Farm (7 miles N.E. of Haltwhistle)
He wed 30 Dec 1778 to Jane Carrick 2nd Sep 1758, d26 Sep 1838.
John's father was Robert - 3rd child of a 2nd marriage. Bapt 4 Jun 1710 at Low Grains, Bewcastle. Died 7 Aug 1800 at Hindley Steel Farm. He wed 1st: Jane Maggee - 11th June 1739 in Haltwhistle. Jane died 1st Mar 1752 at Butterburn Farm. He wed 2nd: Anne Elliot of High Grains on 17 May 1755 at Bewcastle.
Robert's father was James - eldest of at least 5. Bapt 7 Aug 1670, possibly in Spadeadam, died 1732 possibly in Haltwhistle. He wed twice. His father was James Died 1696 at Wrygarth, near Spadeadam. He wed Ann Lowther 30 Nov 1666 at Lanercost. She died 23 Jan 1717 or 18.
Cheers
Bob
PS I haven't verified the earliest names mentioned, but a very trusted and respected researcher did a lot of on site work on this family