Well, there is a relationship between the halting problem and incompleteness, so perhaps an opportunity to read something along these lines will present itself shortly (for certain values of ‘serious’).
One question that has interested me about halting oracles and God’s omniscience: Does traditional everlasting life require God to be a halting oracle? In other words, to create a world that will run forever, does God need to know in advance that it will, in fact, run forever in a halting sense? Possible complication - we don’t know for sure that the behavior of this universe is computable in the Turing sense, and so analysis with respect to Turing machines and halting may not apply.