Thanks for the response. I was trying to illustrate why my argument doesn't work, but you did a much better job at that. I may have found what I've been lookin

Thanks for the response. I was trying to illustrate why my argument doesn't work, but you did a much better job at that. I may have found what I've been looking for in a related topic called Oracle machines for the halting problem. Part of its definition is that it can't solve problem for machines equivalent to itself, which, I believe, would exclude Z-type programs from the domain. To put my plea into some formal jargon, "Just because the halting problem is undecidable doesn't mean oracles Turing machines for the halting problem don't exist." Kind of a simple and obvious point in hindsight, but I'm happy with it.