I have noticed this discrepancy before and you have helped sort it out for me.
The number of regular and National Guard units normally ascribed to Puerto Rico are roughly in proportion to the number of men who were reglars and National Guardsmen.
However, about three-quarters of Puerto Ricans who served in WWII were not regulars or National Guardsmen but draftees, and there are not enough other Puerto Rican units nomally attributed to Puerto Rican draftees to have absorbed most of them. Of the sixteen AAA battalions you list, I have only seen four previously ascribed to the Puerto Rican draft.
There is clearly a wider story to be told about the surrogate use of Puerto Rican troops by the US Army in Latin America in WWII, particularly in the Caribbean. I have seen reference to them in Cuba, Trinidad, Venezuela and the Dutch West Indies, besides on Ecuadoran and Costa Rican Pacific Islands.
I can't help you at all with your research, except to encourage you to dig out more about this untold story.