I think a place to check in Minnesota for Goedert, from Luxembourg, is in Stearns county.There was a settlement in that county where many from Luxembourg immigrated, in the 1850's.That might be the destination the brothers were coming to? Perhaps to relatives who had come before?
There may be records at that church for the brothers?maybe some of them settled down in Stearns county, or neighboring counties, where free homestead land was available.
On the 1880 census, some of those Goedert families show that older ones are born in Belgum.
STEARNS HISTORY MUSEUM STEARNS COUNTY HISTORICAL SOCIETY 235 33rd Avenue South St. Cloud, MN 56301-3752 320-253-8424 Fax: 320-253-2172 Email: firstname.lastname@example.org Executive Director: Charlene Akers http://www.stearns.history.museum/http://www.stearns.history.museum/
Maybe ordering Michael Goedert's death certificate from The Minnesota history center (online for $9) would give you additional information that could help your search.