Given the context, I made the stylistic choice to translate Kaguya-hime as Princess Moonlight as has been done in some actual English translations of the fairy tale.
"Only now that I put on this heavenly coat do I realize my gratitude to you."
No sooner did Princess Moonlight say this than the envoy of the Moon wrapped the coat around her.
And so the heavenly chariot bearing Princess Moonlight disappeared into the sky, as if fading away.
......Thus
Princess Moonlight left this impure Earth and returned to the Moon.
The End.
