My understanding is that the English of Jesus's name would be more accurately Joshua

Not quite. The 'j' sound as we know it today (/dʒ/) was a late development. The most common transliteration of the Aramaic is 'Yeshua'. The first sound/letters here had a compliment in Greek 'Ie(sous)'. And neither Greek nor Latin - the former of which the New Testament itself was written in - had a /sh/ sound.

And those early people who encountered the New Testament texts in Greek - even if they happened to have been aware of what the original pronunciation was in Hebrew or Aramaic - were probably just more comfortable with the regular old /s/ sound.