The 1857 is very detailed and does not seem to be written as a speculative genealogy.The line as I can make out is: Hallgrimur: Petur: Hallgrimur (there is a note on him): Gudmundur (brother is Thorlakr, father of Gudbrandur bishop): Hallgrimur (brother is Sigurdur, father of Helga kona Jon Arason bishop): Sveinbjorn Thordarson.
Somewhere I got information that inserts Thorstein between Sveinbjorn and Hallgrimur so that agrees with your note.
I have part of the Fitjaannall, pages 163 to 288 and see the line on page 236 also giving the death notice of Hallgrimur in 1674.I got this fragment from my grandfather along with the Hymns.I had not searched it very much up to now.I will look further at it and also in Bogi's Syslumannaæfir; which I used for Fjeldsted line.
So now I end up with an extra Hallgrimur as well as Thorstein.But Thorstein is not in the 1857.
I can scan the Inntak if that is any use to you but understand that funds are limited for your work. It was written by Halfdan Einarsson. I will continue to struggle with translaton of it. Thanks very much for your replies.