Ted, I am another Illinois "Kukuk" and am familiar with your family genealogy.I cannot help but wonder if our families are related, but have been searching for over ten years with no luck yet.
My Kukuks emigrated between 1889-1891, proven by birth records and supposedly, according to family lore, they emigrated with seven brothers.But we know of NONE of them nor can we find any records connecting such.
Out of the 20+ identified Kukuk families in the US (I communicate with three active Kukuks who research our name well) there are THREE Kukuk families in IL and apparently all separate and distinct.
If you're looking for a JOHN JOSEPH KUKUK, that's my GGF.There's 700 entries in German listing for JOHN's, but without any knowledge of his home town or emigration records, I am stuck for now.Anyway, saw your listing and just wanted to give this a shot.
Let me know if you have any questions.I believe I even have a few of your family records that I picked up when I lived in Chicago and was ordering birth records.