I have looked in Halfdan Helgason's excelent Genealogy Databasehttp://www.halfdan.is/
And they are in it, going back 62 generations. I don't think that Halfdan reads this forum, just send him an email, explain your details and ask him for a password.
In 1893 Helga Ásmundsdóttir age 57, Sigtryggur Sigurðsson age 18, Ingriður Sigurðardóttir age 14 sailed on the S.S. Lake Huron (I have a picture)from the port of Vopnafjordur.
Born on 22 August 1875 - í Garðstungu í Þistilfirði
* Died on 26 March 1953 - í Wynyard
* Age at death: 77 years old
Married to Soffía Guðrún Gísladóttir Anderson, born on 8 August 1894 í Stekkjarkoti í Gullbringusýslu
I think this looks correct :-)