I'm sorry to ask this question, because it seems very stupid, but how exactly would one create a set-up where a Turing machine, as in head-and-tape style thing, actually interacts with a halting oracle?

I don't doubt that its possible but I can't think of an elegant way to do it.

Ahh, so that's what the <Can someone recall the title of Eliezer's parable in which the genius level humans spend thousands of years deciphering the messages sent by the not-so-smart universe simulators?> were using!