This project seeks to connect Shlomo Zalman Chaim Klein to Maran Yosef ben Ephraim Karo. Shlomo Zalman Klein's mother was Yehudit Stein and she was the daughter of Tzvi Stein which seems to be the connection.
Peretz Tuvia Stein (Fielder) is also related but I am not sure how yet.
Here is some extensive writing on page 29 of this book: [http://www.jgsob.org/aleizikoroin/%D7%A2%D7%9C%D7%99%20%D7%96%D7%9B...].