[Jedd]

> .. we still have records of Josephus Flavius ..

Those writings are doing a lot of heavy lifting, since that's about all apologists can hold up as 'contemporary corroboration'.

Antiquities was written in the last decade of the first century, so at the further end of your 50-60y range. As you note, the wording in the Jamesian reference is not very compelling in itself, and historicists generally argue that Josephus would have explained his terminology much more carefully than we see in that section, so there's some reason to doubt it was in the original.

The longer section from that work that apologists refer to is clearly an interpolation. The style is completely wrong for both the author and the context. The previous pages are describing taxes, protests, massacres, etc and then there's this very brief and spectacularly flowery prose that attests to Jesus being the Christ, and to the ten thousand wonders he did, and then on the next page the author continues with 'And another terrible thing that happened to the Jews ...' -- which only makes sense once you remove the clearly forged / added page.

At which point we're really short - a rounding error away from zero - on any corroborating stories from the 1st century.