In "I'm well" and "I'm good", "well" and "good" are adjectives, not adverbs. That's because you can say "I'm X" when X is an adjective ("I'm happy", "I'm busy") but not when X is an adverb ("*I'm happily", "*I'm busily").
I'm going to argue the toss on this one... In the intended sense (ie in answer to the question "How are you?"), good modifies the verb "to be", hence is an adverb.
You're arguing that the sentence "I am good" is to be understood as being parallel to "I walk slowly". But there are three reasons why I find this interpretation implausible. First, you can't substitute other adverbs for
good (if you try, you get wholly ungrammatical sentences like "*I am happily" or "*I am busily"). Second, you can't substitute other verbs for
am (if you try, you get sentences like "*I exist good" or "*I run good" — these are grammatical in some dialects and registers but not in formal British English). Third, the sentence "I am X" is perfectly grammatical when X is an adjective: you can say "I am tall" or "I am happy".
So my interpretation (in which
good is an adjective) is straightforward and productive, whereas your interpretation (in which
good is an adverb) is forced and unproductive.
You seem to be implicitly relying on a theory whereby a
how question must be answered with an adverb, but surely you wouldn't answer "How was the meal?" with "*It was tastily."