Well, the Gonstad clue didn't help me at all at this point.
However, after hours of looking at this I have a candidate to look at. Here's how I came to speculating about this family. It looks like more than speculation but let's see how this plays out.
In 1870, Betsy's parents are living with her and Christenhttp://search.ancestry.com/iexec?htx=View&r=an&dbid=...
So the parents are Halvor Halvorson and Martha.
There is another Halvor Halvorson on the same sheet with his family. Let's keep him in mind. Doesn't it say Jr. and Sr. on 1880 census? http://search.ancestry.com/Browse/view.aspx?dbid=6742&pa...
I went backward to 1860 and found the alleged Halvor and Martha *P* living with a daughter, Ingri. http://search.ancestry.com/iexec?htx=View&r=an&dbid=...
So there is a Halvor and an Ingri who would be Betsy's siblings.
Betsy aka Bertha was reported to have immigrated in 1850 acc to 1900 census http://search.ancestry.com/iexec?htx=View&r=an&dbid=...
My immigrants book doesn't show a good match. Dates are often not accurate on the censuses anyway so I have to be flexible.
I looked at a passenger list in 1851 and the family 62-67 look very interesting. http://www.norwayheritage.com/p_list.asp?jo=886
ID 456962 Halvor Halvorson 49 m
ID 457063 Martha Halvorson* 45 f
ID 457164 Halvor Halvorson* 18 m
ID 457265 Sigri Halvorsdatter* 16 f
ID 457366 Ragnil Halvorsdatter* 12 f
ID 457467 Paulne Halvorsdatter*
Ages and names aren't perfect but worth looking at. The parents are born about the same time acc to US Censuses - abt 1802. Too late for the 1801 census so I won't find them there.
Hmmm let's look for these kids...