Jeff,
The Swedish name Stina often became Christine in the U. S. And, Anna's and Christine's birth years are the same as those of Daniel's children. Adding the other daughter, Martha, makes even a better fit, but gives no proof. Keep in mind that Daniel's daughter Christine should have come to the U.S. with the family, as she was only nine years old at that time, in 1873.
The family may have taken the name Engstrom when entering this country. There was one other family from a farmstead in the north of Gräsmark that took that name, but it was not a family related to Daniel, or at least seems not to be. This family ended up in western Wisconsin in a township called Star Prairie. It is less than an hour's drive from Minneapolis/St. Paul, and just north of New Richmond, Wisconsin.
I find another Engstrom in Two Harbors, Minnesota. That is up near Duluth. He was Johan Magnusson in Gräsmark and born 1860 [I think really 1859] on Södra Ängen. He took the name John Engstrom when he immigrated in 1886.
I have found some Engstroms in other records from Gräsmark, but they do not seem to be related to Daniel.
I had a phone call about 15 years ago from a man who was an Engstrom. I think he lived in Texas. If I can find that info, I will send it to you. I tried twice to talk with him again, but he never returned my phone calls.
I am also looking for some emigration notes that I took some years ago. This family probably left from Oslo rather than a Swedish port. It is closest. Oslo was still called by it's old name in those days, Christiania.
I am somewhat fluent in Swedish, so let me write in the Gräsmark forum and ask if anyone knows about where Daniel and his family may have ended up.
Hälsningar, Stan