Found this on Ancestry.com:
John Janecek in the 1940 Census. Age: 62, born abt 1878. Birthplace: Illinois. Gender: Male.
Race: White. Home in 1940: River Forest Twp, Cook County, Illinois. Household Members.
Head: Floyd Strickland, 49. Wife: Mildred Strickland, 45. Daughter: Ruth Strickland, 10. Son:
Judson Strickland, 5. Brother: John Janecek, 62.
Can't say if this is the Jan Janáček we are looking for, but it occurs to me that Judson Strickland
may still be among the living and may be able to shed some light on this. Or maybe not.