Since last posting I found Henry's son and my great grandfather William Hagan (1849-1881) getting married in Diocese of Dromore (Tullylish) on 2 May 1868 to my great grandmother Catherine Feenan (aka Feeney) (1852-1910). Per 1870 US Census, William and Catherine and their first child Elizabeth are living on Lonsdale Rd in then Smithfield Rhode Island along with several of William's siblings, most with jobs (even 12 yr old Dan who is working in cotton mill per census). William is considered head of household in census, so conclusively, we can say William and Catherine and many of Henry Hagan's other children came over to Rhode Island from County Down between mid 1868 through 1869 to be so established with residence and jobs by time of census.
Henry Hagan's own immigration date to Rhode Island is shown to be 13 Apr 1871 in his Naturalization filing seven years later.