I'm in agreement with everything you say here. I'm still pondering a few aspects of NPEXP's example (2), though. That is, his first example (2), not his second example (2).
I agree that a preposition needs a substantive for an object, so "more than five months" must be a substantive. More specifically, it appears to be a noun phrase, consisting of the noun "months" modified by the quantifier "more than five", as you said. This position is supported by the fact that the sentence can be shortened to:
1st-2-a: Jack has played the guitar for months.
However, the entire prepositional phrase "for more than five months" is adverbial. The sentence can also be stated without the word "for":
1st-2-b: Jack has played the guitar more than five months.
Now the phrase "more than five months" is adverbial rather than substantive, since it takes the place of the adverbial prepositional phrase in the original example. Is "months" still the head of the phrase? I'm not sure. Let's make one more change:
1st-2-c: Jack has played the guitar longer than five months.
In this example, it seems clear that "longer" must be the head of the adverbial phrase, since "longer than five" can't modify "months" like "more than five" can.