The OP stated in the question that Sītā is portrayed as Rāma's half-sister in the Jātaka.
However, the story of Jātaka in question clearly states that Of his sixteen thousand wives, the eldest and queen-consort bore him two sons and a daughter. So Sita was mentioned as the own sister of Rama-paṇḍita.
Coming to my answer, I had found the following issues worth mentioning:
- The Jātaka tales are a voluminous body of literature native to India concerning the previous births of Gautama Buddha in both human and animal form, dating their average contents to around the 4th century BCE. Many of the Buddhist texts appeared much later to his leaving the human body. So orally transmitted stories might have been altered to suit that age.
Siddhartha, the Gautama married to his cousin Yaśodharā. However, the Dasaratha-Jataka tells about Rama-paṇḍita marrying his own sister Sita. Was there any tradition in ancient/modern India, where children of same parents marrying? Very peculiar. This Dasaratha Jataka may not be reliable.
Though some of the incidents in both Dasaratha Jataka and Ramayana had been quite similar, this Jataka story does end with coronation of Rama-pandita after completion of his exile period, but Ramayana deals with birth of Sita as ayonija, abduction of Sita, elimination of Vali, Search for Sita, Construction of a bridge over ocean, war between Sri Rama and Ravana and finally coronation of Sri Rama.
Further, we have to understand 6 Pramanas, which the teachers of Advaita Vedanta philosophy had codified for resorting to right means, to understand various issues. Which pramana has to be resorted to & also when, is decided by the situation and the nature of object concerned.
The sixth Pramana is Sabda. Sabda pramana is verbal testimony. It is also called ‘apta-vakyas’ (statement of a trust-worthy person), and agama (authentic word).
Saints are considered to be in Union with the God and the words that flow from them will never be untrue. In case of inconsistency in Sastras, the words/advice of saints can be relied upon. The sixth Pramana is Sabda, coming from a trust-worthy person refers to, in my opinion, the utterances of Saints.
Sri Shirdi Sai, a renowned saint, had a talk with one of his devotees. The discourse is as follows:
One devotee of Shri Sai Baba was Shama. Shama was the closest of Sai Baba, and shared a relationship of a closest friend, with Saibaba. Shama would speak with Sai Baba, as a closest friend speaks, quite knowing the stature of Sai Baba.
Once the following incident took place. Shama asked Sai Baba,
"Deva (Shama always use to address Sai Baba by Deva, meaning God) it is written in Ramayana that Lord Rama got a bridge built by 1 crore (10 million) monkeys. This bridge (is called Setu) spanned the sea, so Lord Rama and his troops could cross the sea and reach Lanka. There He waged war with Ravana and vanquished him. Deva, is this true."
Sai Baba replied, "Yes this is true. The sea is real and Lord Rama was really there."
Shama inquired, "Deva, where did so many monkeys sit? And how did they sit?
Sai Baba replied, "They sat on the trees and clung to the branches. They looked like myriads of ants."
Then Shama asked Sai Baba, which perhaps only he could lovingly dare, "Did You see this with your own eyes?"
Sai Baba replied, "Yes, yes I saw them with my own eyes. Alright Shama."
Shama again said what only he could lovingly dare, "When I first saw You, You hardly had a stubble of mustache (a popular way in India to suggest youngsters). Then how and when did You go to see 'Vanar Sena(troops of monkeys) Re.' "
Sai Baba replied, " Shamyaa (as He lovingly called Shama) you and I have been together for many generations. I remember them but you do not."
In wonders Shama asked, "How old were You then?"
Sai Baba, "Just as you see me now."
Shama could not grasp the immensity of this spiritual fact or truth. He persisted, "Is this really true?"
Sai Baba as always, "Have I ever lied sitting here in the Dwarkamai? What I say is true. I swear by you."
So Ramayana did happen. Whether historical evidences of our time support that fact or not, it is immaterial.