Yeru
I would suggest that the Pentegon didn't persue this on it's own initiative, but was directed towards it by the civilian leadership (read Kennedy).
War hawk eisenhauer appointee lemnitzer is a much more likely source for the idea, imo. Jfk's bay of pigs, which took place before this, was half baked, compared to northwoods. Jfk had subsequently begun scaling down vietnam operations and reigning in the cia. Lemnitzer was moved from his position shortly after this affair.
SS