As both sources report, ship movement cards are available from the U.S. National Archives and Records Administration (NARA), specifically from the NARA facility in College Park, Maryland. These are available for any World War II merchant ship having an Armed Guard unit aboard, not just Liberty ships. Ship movement cards constitute voyage reports in that they (to quote from usmm.org) "list ports of arrival, due dates, dates of arrival and departure, and convoy designations. Information you must provide: name of ship, dates of interest," both of which you have.
See also 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 Rick Pitz' experience 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 reported 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 8; see also the usmm.org page mentioned above. Page 7 of the NARA document mentions Navy Armed Guard logbooks which may also be of interest to you. Page 10 of the same document mentions merchant marine vessel logbooks, also of possible interest. Some of the 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. 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 works only if you reside near the facility. Or, as Rick mentions, you can request research assistance from NARA staff, which involves a cost.
Ron Carlson, Webmaster
Armed Guard website www.armed-guard.com