"I'm not quite well enough ready yet" is perfectly acceptable in speech, and a stinker on the page because its middle too sticky to parse without cues of intonation and speed. Correctness is a slippery idea in natural languages, be careful with it!
That said, in brief, it is a declarative sentence with a predicate comprising an adjectival complement. At the core of the complement is the adjective ready. This is successively modified by the adverbial phrase of degree well enough (itself the adverb of degree well modified by the adverb enough meaning sufficiency) and then the adverb quite. The resulting adjectival phrase is then modified again by negating it, leaving another adjectival phrase quite well enough ready, which is then modified again by yet (again leaving an adjectival phrase), which restricts the phrase to mean at the present time not well enough ready yet.
[I] ['m [[not [quite [[well enough] ready]]] yet]]
If you are interested in the process or a detailed explanation:
The overall structure is clearly a declarative sentence taking the form of a subject "I" followed by a predicate "am not quite well enough ready yet". The subject is simple.
The predicate takes the form of a present tense form of "to be" followed by an adjectival complement "not quite well enough ready yet". Such sentences are common and used to declare a state. Clearly in the broadest sense, we have a sentence analogous to "I am green" or "I am happy", where I have used a simple adjective to stand for the adjectival phrase.
The adjectival phrase presents us with a problem in that it can be attacked from both sides "not + adj.phr + yet" is a common construction which "negates for the time being" an inner adjectival phrase: "I am not green yet". The "yet" cannot work with a positive adjectival phrase (*"I am green yet") so if you really need binary division, I would suggest that the phrase is first decomposed into a negative adjectival phrase and the adverb "yet". It is clearly an adverb as you could substitute adverbs such as "today" or "willingly" without changing the structure) ("I am not green today", "I am not sad voluntarily").
As I said, that negative adjectival phrase "not quite well enough ready" is decomposed into an adjectival phrase prepended by a negation. So now we have an even smaller adjectival phrase. "quite well enough ready". We know we still have an adjectival phrase because we can still substitute an adjective, "I am not green yet".
This inner adjectival phrase can be decomposed into an adverb "quite" modifying an even smaller adjectival phrase "well enough ready". We can again test by substituting an adjective "I am not quite happy yet".
"well enough ready" as an adjective phrase decomposes into "ready", an actual adjective (at last!) and "well enough" which functions as an adverbial phrase. We know it is functioning as an adverbial phrase because we can substitute an adverb without loss of structure. "I am not quite sufficiently ready yet". (adverbs commonly modify adjectives, eg. "exceedingly beautiful").
"well enough" is clearly an adverb of degree. It can be analysed (if you must) into the main adverb "well" and "enough" which is an adverb which modifies "well" to weaken it to mean only "to sufficient practical degree". We can see that it's this way round because "well" stands by itself "I am not quite well accustomed yet".