Gandalf at Zirak-zigil

[Dakêsîntrah]

This has probably been touched on before, but I'll throw it out anyway, as I have been rereading through this part and have been contemplating the exact nature of Gandalf's 're-embodiment.'

I know the traditional interpretation is that many think Gandalf's spirit passed out of Middle earth temporal time and was again embodied into the corpse of the old man laying empty at Zirak-zigal.

However, Tolkien never explicitly says it was a 'spiritual re-embodiment' of the original Gandalf as far as I can recall.

['Naked is alas! unclear. It was meant just literally, 'unclothed like a child' (not discarnate), and so ready to receive the white robes of the highest.'] JRRT, 1954, draft letter 156.

Tolkien also stated (same letter) that Gandalf was not sent back by the Valar -- implying it was rather Eru, the 'Authority', as the wizard had passed out of time itself.

This would infer that the spirit "Gandalf" was gone forever and the spirit that replaced him as "The White" was Eru Himself. He was still Gandalf to the physical beings in Middle earth, for Gandalf was only recognizable by his physical shell.

Thoughts?