Playing around with the problem, I think, has increased my understanding of the real World.

In what ways?

Most insights that arise from Newcomb's problem seem to me to be either phony or derivable from simpler problems that don't feature omniscient entities. Admittedly you can meditate on the logical loop forever in the illusion that it increases your understanding. Maybe the unexpected hanging paradox will help snap you out? That paradox also allows perpetual meditation until we sit down and demystify the word "surprise" into mathematical logic, exposing the problem statement as self-referential and self-contradictory. In Newcomb's problem we might just need to similarly demystify the word "predict", as I've been trying to.