While likely not complete, here is some useful information.
I have searched the subscription website Ancestry.com (www.ancestry.com), a site most commonly used for genealogical research. However I know that Ancestry.com has databases listing the names of crew members and passengers aboard merchant vessels that arrived in certain U.S. ports of entry following a foreign voyage. Information on the port of New York is especially extensive.
I found a name resembling that of your grandfather in one record, as Edd J Harmon, identified as a seaman 1st class and part of the U.S. Navy Armed Guard contingent aboard SS CHIEF CHARLOT, on a voyage in the Pacific Ocean in 1944-1945. The ship departed San Francisco in late August 1944 and returned to San Francisco approximately March 15 (exact date not specified), 1945, having departed from Manus Island, one of the Admiralty Islands, also on an unspecified date.
From a separate source I found a fragmentary record of the longer voyage. CHIEF CHARLOT departed Leyte, Philippine Islands, on Feb 6, 1945, and arrived in Hollandia, New Guinea, on Feb 12. This supports your grandfather's statement to your mother that he had been in the Philippines.
Interestingly, I found a record of another Armed Guard sailor with a very similar name, John Edd Harmon. Initially I thought these were both the same man despite the discrepancy in the name, John vs. Joe. However I found that John Edd Harmon was aboard an entirely different ship, in the Mediterranean, at the same time Edd J Harmon was in the Pacific. But the similarity in the names is striking. Do you know of a John Edd Harmon?
CHIEF CHARLOT was a Liberty ship, constructed by Kaiser Permanente Shipyard No. 1, Richmond, California, in 32 days between Sept 19 and Oct 21, 1943. She survived the war and was scrapped in 1958 in Seattle. The ship was named after Charlot (1830-1910), chief of the Bitterroot Salish tribe in Montana, 1870-1910.
Since you know that your grandfather was in the Navy as early as September 1943, it is possible that he was aboard one or more other ships. (I was able to determine that he was NOT aboard CHIEF CHARLOT on its next earlier voyage.) But I have found only the single voyage described above.
Because there may have been other ships, you might wish to attempt to obtain a copy of your grandfather's complete military service record. His record would provide additional details, including other ships to which he was assigned. Please see this page from the Armed Guard / Merchant Marine website that I manage: http://armed-guard.com/searchmil.html, in particular section II.A.1. - Records of Individuals - U.S. Military. You will have to contact the National Personnel Records Center, a U.S. National Archives and Records Administration (NARA) facility in St. Louis, MO. Provide as much identifying information as you have. There may be a charge for research time, photocopying and mailing, but the Records Center staff will provide an estimate on the cost before beginning work.
It would be best if the request came from your mother, if she is living, or an aunt or uncle on your mother's side, rather than from you. As a child of your grandfather your mother (or aunt or uncle if also a child of your grandfather) is next-of-kin to your grandfather. (Next-of-kin = parent, spouse, sibling or child.) A next-of-kin can obtain the full military service record whereas someone not next-of-kin, such as yourself, may not be able to. Of course you can do the leg work in preparing a request but the request should be signed by a next-of-kin. If there is no living next-of-kin, then make the request yourself and hope for the best.
Ron Carlson, Webmaster
Armed Guard / Merchant Marine website