Does this prove that Uttara kanda may have been a later interpolation, as phala shruti comes before Uttara kanda.
Ramayana retelling vanaparva-272-289
One possible reason is there maybe a version of Rāmāyaṇa even before Vālmīki came up with his and that's the version presented in the Mahābhārata.
This is what C.R. Sarma says in his book The Ramayana in Telugu and Tamil, A Comparative Study:
Some of the traditional scholars too feel that the present version of the Ramayana is a later development of the original Ramayana which was concise. It is believed that Valmiki the Prakrit grammarian who is said to have lived in the second century A.D., may have developed the brief story of the original Ramayana into a big epic. It is also suggested that the present Ramayana was composed on the basis of the original Ramayana and the Ramopakhyana (story of Rama), as found in the Vana parva of the Mahabharata (chapters 273-291). Macdonell also felt that the Ramayana 'attained its present extend by the end of the second century A.D'.
Varied are the views expressed by the scholars, both in the East and the West regarding the period of the original Ramayana. However, the critical consensus suggests the 3rd century B.C. as the probable period.
The Ramopakhyana of the Mahabharata also deserves a careful study since it is believed to have given an incentive to the recasting of the Ramayana of Valmiki itself, in accordance with the new theory of Rama's being an Avatara of Vishnu. It represents Rama as an incarnation of Vishnu and Sita as Janaka's own daughter. She did not enter fire to prove her chastity. Further, the stories of the Uttara kanda are not mentioned in it. In view of the above, it is believed that the Ramopakhyana may have helped in recasting the Ramayana story.
Peter Scharf in Rāmopākhyāna: The Story of Rāma in the Mahābhārata: an Independent-study Reader in Sanskrit also suggests that the divinity of Rāma in the present day Rāmopākhyāna was not part of the original Rāmopākhyāna when it was added to the Mahābhārata.
I. C. Textual Limits to the Divine Dimension
Textually, the divine dimension of the story is not well integrated into the narrative of Rāma either in the Rāmāyaṇa or in the Rāmopākhyāna. In both it is narrated in peripheral sections forming later additions to the text. Moreover, the narration of the story in response to Yudhiṣṭhira's question whether there is any man (nara) less fortunate than he (257.10) affirms Rāma's humanity and suggests that the story did not include its divine dimension when the Rāmopākhyāna was inserted into the Mahābhārata.
I. C. 2. Limits in the Rāmopākhyāna
The Rāmopākhyāna never explicitly identifies Rāma with Viṣṇu. While Brahmā mentions the incarnation of Viṣṇu in human form (260.5) and enjoins the gods to progenerate sons in bears and monkeys to be his companions (260.7), he does not specify the human form or forms in which he incarnates. Similarly, the Rāmopākhyāna does not include the reentrance of Rāma or his brothers into Viṣṇu's body. It ends with the return of Rāma, Sītā, and Lakṣmaṇa to Ayodhyā, followed by Rāma's coronation, and his performance of ten Aśvamedha Vedic performances. It does not include the contents of the Uttarakāṇḍa, a late addition to the Rāmāyaṇa, in which Rāma banishes Sītā when he learns of rumors criticizing him for accepting her back after she had been with another man. When all the gods arrive upon Rāma's initial rejection of her after Rāvaṇa's defeat, Brahmā tells Rāma that in slaying Rāvaṇa he has brought down an enemy of the gods (275.30) and carried out a great obligation for the gods (275.34). He even goes so far as to address him, "immortal-like one" (275.34), but he does not identify him with the absolute or with Viṣṇu. In fact, the only other mention of Viṣṇu in the Rāmopākhyāna is as the presiding deity of the constellation under which Rāma is consecrated king upon his return to Ayodhyā (275.65).
To summarize the above arguments;
There was an original Rāmāyaṇa (OR) describing the actual events of Rāma's life.
This OR formed the basis for the (original) Rāmopākhyāna that was part of the Mahābhārata.
Vālmīki came along, took inspiration from events of the OR and also the Rāmopākhyāna and created his own Rāmāyaṇa, the Vālmīki Rāmāyaṇa (VR).
There was another edit to original Rāmopākhyāna (after VR was authored) that introduced the divinity of Rāma into Rāmopākhyāna/Mahābhārata.