Lord Shiva is mentioned at many places in the epic, for example when Rama breaks Shiva's bow Lord Parshurama talks about the Lord having used it to destroy Tripura and he is also mentioned as having given boons to Ravan.
But he also appears directly at the time of the Agni pariksha along with the other gods as mentioned in the Yuddha Kanda Sarga 117:
Thereupon, Kubera the King of Yakshas, Yama the lord of death together with the deceased ancestors, Indra the lord of celestials Varuna the lord of waters, the illustrious Shiva the great deity who bears the device of a bull as his banner and having three eyes, Brahma the creator of all the worlds and the best among the knowers of sacred knowledge all these together reaching the City of Lanka in aerial cars, shining like the sun approached Rama.
The text further states that ALL the gods addressed Rama as the Supreme One:
Lifting their long arms, their hands decked with ornaments, those excellent gods thereupon, spoke (as follows) to Rama who stood there, making a respectful salutation to them with his folded hands.
"How do you, the maker of the entire cosmos, the foremost among those endowed with knowledge and an all-capable person, ignore Seetha who is falling into the fire? How do you not recognize yourself to be the foremost of the troop of gods? Among the Vasus, you are the Vasu, named R^itadhama who was formerly the self-constituted ruler, the first creator of all the three worlds and the lord of creatures."
"You are the eighth Rudra among (eleven) Rudras and the fifth (Viryavan by name) among the Sadhyas (a particular class of celestials belonging to Gana Devata). The twin Aswinis are your ears. The sun and the moon constitute your eyes. O the destroyer of the adversaries. You are seen (to exist) at the beginning and at the end of creation. Yet, you ignore Seetha, just like a common man."
Hearing the words of those guardians of the world, Rama, the lord of creation, who was born in Raghu dynasty and the foremost one among protectors of righteousness, spoke to those god-chiefs as follows: "I think of myself to be a human being, by name Rama, the son of Dasaratha. You, as a gracious Divinity, tell me that which I as such really am like this.”
It is then that Brahma addresses him as the Supreme Brahman that you mentioned in the question and I am skipping that part since it is not relevant here. However Shiva does later address Rama directly as described in the Yuddha Kanda Sarga 119:
Hearing the auspicious words thus spoken by Rama, Lord Shiva the Supreme Lord thereupon delivered the following still more beautiful speech: "O lotus-eyed, long-armed, broad-chested, annihilator of enemies and excellent among those upholding the cause of virtue! Thank heaven! You accomplished this task. Fortunately has the fear born of Ravana - which increased the severe darkness on the entire world has been removed by you, on the battle-field, O Rama!"
So to answer your question, the Valmiki Ramayan does not explicitly portray Lord Shiva addressing Shri Rama as Vishnu or Narayan though he is mentioned in the group of gods who address him that way and he is very much present when Brahma is addressing Rama in that manner as well.
