'the cleanest' vs 'cleanest': article-containing adverb phrases?

Question

We have two phrases structures:

1. 'the nicest in my school'
2. 'the cleanest in my house'

These phrases can act as nouns or adverbs:

1. 'He is the nicest in my school.' - noun phrase.
2. 'She cleaned the cleanest in my house.' - noun phrase -or- adverb phrase. Meanings (noun phrase: "She cleaned the cleanest [omitted thing] in my house; adverb phrase: "She cleaned most, comparatively, [to the other omitted things] in my house.").

So these are the disambiguations I suggest:

1. 'She cleaned cleanest in my house.'
2. 'She cleaned the cleanest, in my house.'
3. 'She cleaned the-cleanest-in-my-house.'

Isn't 1. a better disambiguity to simply say she, herself, is the best cleaner? Because in 2., 'the cleanest' can also be a noun phrase and in 3. 'the-cleanest-in-my-house' is in emulation of another person?

About 1: 'in the house' is a location set by the adverb so there is an ambiguity; however, when setting groups by the adverb (i.e., 'of my house'), 1. is sufficient, right?

Update

Additional disambiguities:

1. She cleaned, the cleanliest in my house. - Uses allusion to suggest that the subject, herself, is the cleanliest person.
2. She cleaned [the] cleanliest in my house. - Shows that 'the' is unnecessary. Perhaps, for example, it is added for euphonic purposes.

Answer 1

I'm still straggling to grasp what disambiguation this question seeks, but it touches a number of topics I would like to discuss:

1. Noun phrases versus adverbial phrases
2. Omission of [the] in the use of superlatives
3. Ambiguity

1. Noun phrases versus adverbial phrases

StoneyB discusses here the terminology prepositional phrase versus preposition phrase and I think it's worth reading. Your question uses the terms noun phrase and adverbial phrase as two opposed terms, but this is not necessary the case. Both phrases:

• the nicest in my school

• the cleanest in my house

are noun phrases because the main word in the phrase (nicest and cleanest) is a noun. However, if one looks at the function of these phrases within a sentence, then:

• He is the nicest in my school

is a subject complement because it attaches an attribute to the subject. And:

• She cleaned the cleanest in my house

is an adverbial complement because it complements the verb by describing how she cleaned.

2. Omission of [the] in the use of superlatives

phenry discusses here that when using the superlative the is frequently omitted but implied (e.g., "I like this one [the] best").

If I understand your question correctly, you argue this may be a source of ambiguity. I'm not sure how.

3. Ambiguity

Your question doesn't describe how this ambiguity works, but let me guess, you argue that in the sentence She cleaned the cleanest in my house it is possible to interpret:

1. the cleanest in my house as a single adverbial complement, i.e. she cleaned in the cleanest way that is possible to clean your house.

2. the cleanest and in my house as two separate adverbial complements, i.e. she cleaned in your house and she did it in the cleanest possible way.

As you see the difference in meaning is so subtle that I would argue both interpretations convey the same meaning and there is no need for desambiguation.