From the Statue of Liberty - Ellis Island Foundation, Inc., I did discover that a William Kamphenkel, age 19 & single, arrived at Ellis Island from Copenhagen, Denmark on May 22, 1923.
If you do a quick Kamphenkel name search, you will discover that a William Kamphenkel resides (or used to) in Illinois. (I believe there is also a listing for him in Florida).He was a pastor, but I believe that he is retired (to Florida?).I do not believe that he is old enough to be the William who arrived in 1923, however, it is quite possible that this William is his son.
I am related to the Minnesota "Kamphenkel's" who emigrated directly from Germany and thus I do not know William's clan personally.
Good luck in your searching.I hope this might help a little.