If you feel confident about the 28th Street locale, check the "Official Catholic Directory" for the appropriate year. The New York Public Library has a set of volumes, which it catalogs under the main entry, "Cath Dir and Alm."
But also consider checking the New York State Census of 1905. The Manhattan portion is at the New York County Clerk, who has a card index of street addresses to use as a finding aid.
There was mention in a 1909 source of St. Michael's Home for Destitute Children, at Green Ridge, Staten Island, with a house of reception on West 34th St., Manhattan. This home is discussed on page 255 of the 1982 book, "Adoption Agencies, Orphanages and Maternity Homes : An Historical Directory."