Army and Navy Journal (March 3, 1928), p.529:

       "SEEK ORIGINAL WORDS OF FAMOUS MARINE CORPS HYMN.

"MAJ. GEN. JOHN A. LEJEUNE, U. S. M. C., Commandant of the Marine Corps, is anxious to secure the original words of the Marine Corps Hymn. Headquarters, U. S. Marine Corps would be delighted to hear from anyone who can furnish the original version and letters are now being sent out to various retired officers who are believed to have information on the subject. The original hymn verses were composed around 1900 in the Philippines and China by members of Major Waller’s command."

This comports exactly with what I've been posting, though the specific reference to the command of Maj. (later Maj. Gen.) L. T. Waller (1856-1926) is new and seemingly definitive.

Waller served in the Boxer Rebellion, at Cavite, and then in Panama - precisely the sequence of place names in the "Hymn." In 1911, he was at Guantanamo Bay with Henry C. Davis, who wrote additional lyrics.

It's thus conceivable that Waller himself wrote the original verses, though how they were set to Offenbach's music is still a mystery.