As discussed under the Words of Mormon 1:14, the original text permits many thousand but only when directly followed by a noun, such as “many thousand lives” (in Alma 28:10). When postmodified by a prepositional phrase headed by of, we always get the plural thousands (“many thousands of X”). Here in Alma 37:9, the 1830 compositor accidentally set “many thousand of the Lamanites”. The subsequent 1837 edition restored the correct thousands.
Summary: Maintain in Alma 37:9 the plural thousands in “so many thousands of the Lamanites”, the reading of the manuscripts; usage elsewhere consistently supports the plural thousands in “many thousands of X”.