Perhaps in the counterfactual where the logical coin is the opposite of what's true, the calculator should be assumed to also report the incorrect answer, so that its result will still agree with Omega's. In this case, the calculator provides no further evidence, there is no point in using it, and you should unconditionally pay up.

Yeah, that's pretty much the assumption made in the post, which goes on to conclude (after a bunch of math) that you should indeed pay up unconditionally. I can't tell if there's any disagreement between us...