I tried to send this to your email address, but it got kicked back, so I hope you still check this website. I might have some information on Roman Plucinski and his family. I am also a Plucinski descendant (fraternal grandmother), and so I have = information on a large number of Plucinskis in the Chicago area.
Here is the information I have on a Roman Plucinski, spelled Pluczynski, in Illinois:
Roman? Pluczynski, Born Oct 1868 Germany (age 31 in 1900 census), immigrated to US 1881, Naturalized before 1900, wed 1891? (wed 9 yrs in 1900) Jennie ? // Jennie Born Jan 1872 IL (age 28 in 1900 census), had 5 of 5 kids in 1900 census, lived Washington County, Ashley IL? in 1900.
Their children were listed as follows:
Rome J. Pluczynski B Oct 1891? IL (age 8 in 1900 census) Theodore A. Pluczynski B Jan 1892 IL (age 7 in 1900 census) Joseph G. Pluczynski B May 1895 IL (age 5 in 1900 census) Frank S Pluczynski B Sep 1896 IL (age 4 in 1900 census) Helen W. Pluczynski B Sep 1899 IL (age 9mo in 1900 census)
Roman's wife's name is Jennie, not Julia, but this information came from the 1900 census, and names were often misspelled. I attached the 1900 census record so you can look at it. Other records showed that his first name was Roman, not just R.
I have other Roman Plucinskis in my database, but this one had = children's names that pretty much matched with your list. I hope this information is helpful.