I think I really don’t see what the intuition behind the suggested strategy is.
The standard proof of Löb’s theorem as I understand it can be obtained by trying to formalize the paradoxical sentence “If this sentence is true, then C”. Intuitively, this sentence is clearly true, therefore C. (This of course doesn’t work formally, what is missing is exactly the assumption that you can conclude C from a proof of C).
With your suggested proof, I just wouldn’t believe it’s a proof in the first place, so (for me) there’s no reason to believe that it should work. If you can explain in more detail what exactly you would like to formalize, I would be curious.
I was interpreting things somewhat differently:
“this” should be a reference to the Gödel code of the current proof
the OP would like to have what is essentially an application of the diagonal lemma to the whole proof instead of a proposition
“zip”/”unzip” is simply taking the Gödel numbering, and doesn’t hide any extra complexity
In this case the problem here is making precise what one hopes for in step 2. (I don’t really see how one would do it), and then to prove that one can make it work.