Piscean -
I'm glad you brought up the distinction of form and function because this goes precisely to the heart of what I'm trying to show.
Look - in the example phrase Speak a little louder, the word louder may look like an adjective (in form) but it is functioning as an adverb. Isn't this the whole point of the discussion?
Now what I think I'm contributing to the thread is this: When we use the term 'adjective', we are referring to the grammatical role of a word/phrase in use. This is its function, which, for an adjective, might be to modify a noun. This is why, in my judgement, the form is irrelevant. So for me a word cannot be both an adverb and an adjective simultaneously, but can serve only one of these functions in any one instance, as it stands in use. In our example it doesn't matter that louder looks like an adjective because it isn't.
Regarding dictionaries - they're not telling you that there's an adjective fast and an adverb fast, as if they're two different words. They're saying that there's one word with two different uses - either as adjective or adverb.
If you disagree with anything I've said, could you please explain how.