Thank you for sharing this. These are all excellent points.
I especially like this:
In the absence of the preposition "for," I'd be inclined to say that "more" (which is an adverb) is the head of the adverbial adjunct. However, a noun can be the head of an adverbial. Although this is less frequent than the prepositional phrase with "for," I think we can use "five months" as an adverbial, especially in the presence of another adverbial, don't you agree?
I was (and am) also inclined to consider "more" the head of the adverbial, in parallel with the "longer" version. But the fact that the simple noun phrase "five months" puts an intriguing twist on things.
And it doesn't even need the presence of another adverbial. I can say "I waited there an hour", so why not "He played the guitar five months"?