Nor do I know of any fictional characters that are so deliberately placed recent history and yet their existence is believed by their contemporaries as real.
How about Huangdi?
"Throughout most of Chinese history, the Yellow Emperor and the other ancient sages were considered to be real historical figures. Their historicity started to be questioned in the 1920s by historians like Gu Jiegang, one of the founders of the Doubting Antiquity School in China. In their attempts to prove that the earliest figures of Chinese history were mythological, Gu and his followers argued that these ancient sages were originally gods who were later depicted as humans by the rationalist intellectuals of the Warring States period. Yang Kuan (楊寬), a member of the same historiographical current, noted that only in the late Warring States had the Yellow Emperor started to be described as the first ruler of China. Yang thus argued that Huangdi was a late transformation of Shangdi, the supreme god of the Shang pantheon.
[snip]
Most scholars now agree that the Yellow Emperor was originally a deity who was later transformed into a human figure."
I said placed in recent history, and contemporaries. The Yellow Emperor seems to have been placed millenia in the past, compared to when belief in him existed.
The proper comparison of the Yellow Emperor would be someone like Noah or Enoch - someone placed many centuries or even millenia in the past of when he was known to be believed in -- and I certainly would consider Noah and Enoch to be most likely fictions, never to have been based on real people at all.
Jesus is a different sort of fish altogether.
To break up the awkward silence at the start of a recent Overcoming Bias meetup, I asked everyone present to tell their rationalist origin story - a key event or fact that played a role in their first beginning to aspire to rationality. This worked surprisingly well (and I would recommend it for future meetups).
I think I've already told enough of my own origin story on Overcoming Bias: how I was digging in my parents' yard as a kid and found a tarnished silver amulet inscribed with Bayes's Theorem, and how I wore it to bed that night and dreamed of a woman in white, holding an ancient leather-bound book called Judgment Under Uncertainty: Heuristics and Biases (eds. D. Kahneman, P. Slovic, and A. Tversky, 1982)... but there's no need to go into that again.
So, seriously... how did you originally go down that road?
Added: For some odd reason, many of the commenters here seem to have had a single experience in common - namely, at some point, encountering Overcoming Bias... But I'm especially interested in what it takes to get the transition started - crossing the first divide. This would be very valuable knowledge if it can be generalized. If that did happen at OB, please try to specify what was the crucial "Aha!" insight (down to the specific post if possible).