if you are not familiar with Archive.org they have digitized many resources out of copyright as well as a lending library. If you search the category Texts using the search term “Jews in Chicago” in metadata you will find astounding documents. Landsleitschaften and Synagogues are reviewed in “Bridges to an American City” by Sidney Sorkin. There are other resources dating back to before the religious conferences convened in connection with Chicago’s Columbian Exposition in 1893. There are also a variety of Annuals and Directories that you’ll find useful.
I do not know if individual synagogues will have records but it is likely Spertus Institute has collections. Spertus (as well as the IL Secy of State) have libraries online with full-text of The Sentinel, Chicago’s English language Jewish newsmagazine. Searching for surnames in it may turn up business’s ads, and a variety of social items.
Hope these resources will be helpful.
KARLINSKY in Motole, Ivanava, Pinsk, USA and Canada
RAJCZYN in Zhitomyr
SAUWER in Buenos Aires, Argentina and Belem, Brazil