In what timeframe was Jataka tales added to Kuddaka Nikaya?

I am trying to see whether the presence of certain characters and stories in the Jataka tales can be taken as a proof for them (stories and characters) being known in that form in the time of the Buddha. So, the question is different from the other thread on this forum Does Theravada Buddhism accept Jataka Stories? though related. I would assume that even the commentary portion of the Jatakas are based on some authentic source. Yet, is there a way to know by when these stories (the prose portion of the Jatakas) were added to Kuddaka Nikaya? Was it by the first council, or later? Does the author of the prose portion affirm that his commentary is based on an oral linage of the narration coming all the way from the Buddha? Since some of the characters in the Jataka tales (such as Dasaratha Jataka and Ghatapadita Jataka) are seen in non-Buddhist literature in India, and often developed into dramatic stories later, the scholars in India are divided in three ways: a) Independent folklore of the time inspired such stories in both the Buddhist and non-Buddhist sources. b) Buddhist sources, just like the Jain sources are re-interpreting stories from the epics that were already fully developed and existent, and using it to support their respective philosophies. (I would not like to take this position because the Buddhist versions of the stories are much less dramatic and have not taken an epic-like narration. I don't see any motivation for the Buddhists to make the story less attractive if a more dramatic version was already available.) c) The Buddhist Jataka tales and other unrelated stories would have inspired some others to later connect them together, modify the characters and develop grand epics such as Ramayana and Mahabharata. And, some characters were glorified later through they were ordinary characters in the Jataka tales. (Most people do not think in this line. However, I find this more justified. However, to prove this, it is important to know what is the general consensus within Buddhism and particularly Theravada regarding the date of origination the Jataka commentaries.