Just dropping a bit of a flag here:
I’ve long been sceptical about the idea that the Johannine ego eimi Sayings constituted an allusion to the Divine Name or Divine identity; it seems to derive a lot of its fascination from readers who encounter the expression in translation (and Christian readers), rather than directly in Greek or Hebrew. That’s not to suggest a fault in scholars who manifestly read in the original, by the way, but to flag up the existence of a base of popular support among non-readers.
Anyway, as I work through the two works I take to be most relevant — Catrin Williams’s ‘I Am He’: The Interpretation of Anî Hû in Jewish and Early Christian Literature and Jason Coutts’s “My Father’s Name”: The Significance and Impetus of the Divine Name in the Fourth Gospel, I’m struck by the phenomenon of avoidance and circumlocution with respect to the Name. That is: we can easily see that in the first century, authors avoid using the Divine Name altogether — it never appears as such in the New Testament, for instance — and has become the object of circumlocution or substitution. Rather than reading ‘I am’ and pondering whether it refers to the Name, then, I wonder whether it wouldn’t be more productive to see whether ‘I am’ can be seen to function as a substitute or circumlocution for the Name, or (if it is as ‘blasphemous’ as some readers of GJohn want to propose) whether we can find signs that it too is the object of avoidance.
I haven’t thought this through yet, and haven’t finished reading Williams or Coutts, so they may cover this later on. It just strikes me as a possible trajectory for further investigation.