Thanks for your interesting post. Are you saying that formulas have recently been developed implementing Hofstadter's "strange loops" theory?
As recently as last year, in a new forward to GEB, he was complaining that his theory of consciousness and AI was not being taken seriously enough in the field.
While I've never framed it like this, there is a close analog to Hostadter's Strange Loops implicit in the operation of this new class of state machinery that is being described. It is just one dimension however, and not the core principle (it would be difficult to construct useful computing machinery on that theory alone). Hofstadter's strange loops were not a goal in the mathematical derivation, but an analog emerges as a consequence of it.
While GEB is still very highly regarded in the AI community, it is considered more of a brilliant primer than an advanced text. Sadly, Hofstadter's later works fell short of his original. I still have fond memories of GEB, though I haven't read it in at least a decade.