You are missing something important. But you are also adding something. What you are adding is that you are taking the Jātaka's literally. What you are missing is that these are simple morality stories that are not meant to be taken literally. They illustrate principles. In fact they are not even particularly Buddhist since many of the stories occur in both Jain and Vedic literature as well. They are just a way of conveying values in a way that uneducated people can appreciate.
Modern treatments of religion veers away from taking the words of religious texts on face value. There is no reason, except for uncritical acceptance of religious stories, to believe that anything preserved in a traditional text is "the word of the Buddha". When the material involved supernatural beliefs such as rebirth then we have even less reason to take such texts on face value. In the case of the Jātakas the very strong implications of personal continuity between lives conflicts with the fundamental metaphysics of Buddhism which deny the possibility of any kind of personal continuity. Such continuity as might be discerned is entirely impersonal. The fact is that this metaphysic produces unworkable morality and so early Buddhists maintained a doubt standard - arguing vociferously against personal continuity in more theoretical texts, and tacitly allowing for strong forms of personal continuity in morality stories. The contradiction is never acknowledged in traditional texts, never noticed by modern Buddhists, and seldom discussed even by scholars of Buddhism.
Apart from the outright doctrinal clashes and the supernatural elements, especially of the Jātakas, there is the kind of historical conflict that is embedded in the question: events that are supposed to have happened in a particular time frame that physically cannot have happened in that time frame.
The Jātakas as a body of literature use miracles and other supernatural occurrences to create compelling narratives for the communication of Buddhist values. Until the twentieth century the Jātakas remained some of the most revered Buddhist texts and the main vehicle for communicating morality in tradition Theravāda countries. However, precisely because of the supernatural elements the texts have never been as popular or significant in the West.
As long ago as 1748, philosopher David Hume wrote:
"...no testimony is sufficient to establish a miracle, unless the testimony be of a kind, that its falsehood would be more miraculous, than the fact, which it endeavours to establish..."
Certainly the testimony of the Jātakas fails this simple test. It would certainly not be miraculous if the Jātakas turned out to be fictions. However we can re-evaluate the stories as myths which use people in unusual circumstances, performing incredible deeds of magic and supernatural power, in order to convey values. According to Evolutionary Psychologist Justin Barrett imbueing a story or character just enough counter-intuitive properties makes the story memorable and interesting. A figure like the talking wolf in the story of Little Red Riding Hood was probably never intended to be taken literally. Even if we reject the idea of a talking wolf, the story retains a certain fascination as a act of story telling. A story need not be the literal truth to elicit an emotional response.
Thus taking the Jātakas at face value as literal accounts of history are naive at best. The question could only arise as part of a literalist/fundamentalist worldview in which miracles are in fact routine rather than miraculous. But this is far from tenable outside of a religious milieu which allows members to reinforce false beliefs and rewards members for reciting them. As another modern Psychologist, Daniel Kahneman, has said:
“We know that people can maintain an unshakable faith in any proposition, however absurd, when they are sustained by a community of like-minded believers.”
For anyone with a Western education the question of the literal truth or reality of the Jātakas seldom arises, because miracles and magic are rightly not part of our worldview. The major contribution of the European Enlightenment was to free people from the tyranny of religious dogmas and ordinary superstitions. Which we largely see as an important element of the progression of civilisation. That some Buddhists abandon reason to embrace the magical thinking and superstitions of Classical Buddhism is a quirky feature of modern Buddhism, but fortunately not very widespread. Most Buddhists are content to read the Jātakas and myths - fictional stories which communicate a set of important values.