Dear Reinhard,
I think the spelling from polish spelling Szymura to Schumura because of phonetics. The surname is pronounced like this " Che-mura. " With the SZ having a Ch sound and the y having sort of a short E sound is the best I can describe pronounciation.
I had heard/read? somewhere that many of the Polish living in Germany and/or German territories had the surnames changed to a more German spelling. So spelling of Schumura seems logical to me.
I needed an in-law who speaks a bit of polish tell me how to pronounce it. 
Michelina Szymura married name was Pawlak/Pavlock. And actually I believe she came to the U.S. about 1883. This is an assumption per census information of her daughter Mary Pawlak who is listed as from Posen, Germany, Prussia, Aust Poland...
Michelina Szymura-Pawlak (by deth cert)
b. 28 Sept. 1836 Europe
m. John Pawlak date unknown
D. 28 Dec. 1922 - Beaucoup, Washington, Illinois. U.S.A.
Buried 2 Feb. 1923 Mount Olive Cemetery, St. Louis, Missouri. U.S.A.
Father name John Szymura
Mother name Suzie ???
Strange that she was buried so long after she died. I guess the ground was too frozen or something) Her death certificate does list Mount Olive Cemetery, St. Louis and information given about her was given by known relatives also later buried at Mount Olive.
daughter
Mary Pawlak/Pawlock/Pavlock
b. 1867 - Posen/Germany/Aust Poland/ Prussia
d. 22 Feb. 1951
buried Mount Olive " "
To U.S. 1883 so assume she probobly came with her parents. Have not yet found passenter list. Data per U.S. Census Washington County, Illinois.
I believe Michelina Szymura-Pawlak had other children as her daughter Mary Pawlak-Krawiecki obituary mentions she was a grandmother, great-grandmother, sister, sister-in-law, and aunt. I don't know their names though.
I am interested in living Schumura. Always a possibility that a living family might have data though I don't have a clue of the village in Poland she was from. Perhaps one of the families you know might recognize the name Szymura associated with Pawlak or Krawiecki or having relatives who lived in U.S.A. Missouri and Illinois.
Warmest Regards,
Barbie
St. Louis