For a possible source of information, see this page from the excellent web site, American Merchant Marine at War: http://usmm.org/contact.html#contact1
In addition to the possibility of obtaining information about the MANGORE directly from the American Merchant Marine at War webmaster, the website mentions information held by the U.S. National Archives and Records Administration (NARA) facility in College Park, Maryland. Specifically, the NARA Modern Military Records Unit in College Park maintains a number of records that may be of use to you, including ship movement cards, Armed Guard officer reports, Armed Guard logbooks and ships' logs.
Ship movement cards or movement report cards list ports of arrival, due dates, and dates of arrival and departure, among other information. In your case, ship movement records for SS MANGORE should confirm whether she was in Boston on April 13, 1945. See http://www.archives.gov/research/guide-fed-records/groups/178.html and scroll down to 178.4, Records of the Division of Operations. This page suggests that ship movement cards are available only for the period 1917-1940 but I believe (and the experiences of others bears this out) that the availability of such records extends through World War II. The same page states that service records of shipboard personnel are available for the period 1917-1949.
NARA also has Armed Guard reports in which the commanding officer of each Armed Guard unit deployed on a merchant ship prepared a report at the end of a voyage, providing information including the names of the Armed Guard crew for that voyage. See http://www.archives.gov/publications/ref-info-papers/109/modern-military-records.pdf and scroll to page 103. Page 102 of the NARA document mentions Navy Armed Guard logbooks which may also be of interest to you.
Page 105 of the same document mentions merchant marine vessel logbooks, also likely of interest to you. Some merchant marine vessel logbooks are held not at the Maryland facility but at NARA regional facilities across the United States for ports (where a given voyage ended) served by that region. If there had been a collision between MANGORE and another vessel in Boston, particularly a serious collision, that voyage of the MANGORE may have ended in Boston and her logbook may be in the New England regional NARA facility in Boston. Certainly a collision with another vessel would have been mentioned in the log of the MANGORE. See http://www.archives.gov/locations/ for the location of NARA regional archives.
One can do research at NARA facilities in person free of charge, other than photocopying expenses, but obviously that is feasible only if you reside near the facility or can travel to the facility. Or you can request research assistance from NARA staff, which involves a cost. Contact the Modern Military Records Unit at this address:
Modern Military Records Unit
National Archives at College Park
8601 Adelphi Road
College Park, MD 20740-6001
Ron Carlson, Webmaster
Armed Guard website www.armed-guard.com