Sorry, I didn't run into any Holst or Madisons while doing this family research. Nor did I find any branch of these in Illinois, although they could have had relatives there. Generally, the surname is not real meaningful because it is a partronymic and a common one out of Scandinavia simply meaning "son of Mads" and since the Scandinavians did not really adopt surnames until after the turn of the century (the law required it in 1860s but most families simply didn't make the change that early) it is not an indicator of a family relationship if people share the same surname out of Scandinavia. I will keep my eyes open for Holst, which is probably a German name and might mean that your ancestors originated in the Schleswig-Holstein duchies on the border with Germany where many Danes and Germans intermarried. After those wars, many Danes fled the area and came to America, the 1880s being a period of mass migration out of the Duchies. You might want to do some reading on the history of these Duchies just to be prepared to put some of your future research in context. Hope some of this helps!