I reviewed the 1940 census you mentioned.
I noticed that the young women, who were inmates at the Home of the Good Samaritan," were single and there were a few infants also listed with them...some with the same surnames as the girls.
I then googled "'Good Samaritan' Louisiana" and confirmed that it was actually a maternity home.
The woman listed as a "motrow" was actually the "matron." Her place in the household was mistranscribed. She is also listed as "matron" as her occupation.
I believe you will be able to find lots more info, but your 3rd great grandfather, Rev. James Robert DOWNS, appears to have been serving unwed mothers and, perhaps, helping in adoptions.
Best wishes in your search.