Sometimes, the best help arrives when you’re not even looking for it.
I was searching on newspaperarchive.com (thanks to a tip from my friend Sarah) and browsing through the Stevens Point Daily Journal from Wisconsin. I ran across an obituary for Joseph Stroik. I’m not even sure this man is the same one that’s in my tree, but I was amazed at the first line in his death notice:

The Gazette, Stevens Point, Wisconsin (16 OCT 1912)
Retired Farmer is Dead.
Joseph Zdrowski, or Stroik, as the name is commonly called, died at his home, 912 N. Second street, on Monday of last week and was buried from the Polonia church Thursday. He was about 65 years of age and had lived on a farm in Sharon township until five years ago. The cause of Mr. Stroik’s death was cancer of the liver and other complications, with which he had suffered more than a year. He was twice married, his first wife dying several years ago, leaving four sons and three daughters, all of whom are well-to-do residents of Sharon. The present Mrs. Stroik was formerly Mrs. Gudapof this city, whom he married about five years ago.
Incredible… I have been researching the Stroik surname for several years now, and I have never heard the surname referred to as Zdrowski. This opens a brand new opportunity for searching!