If I wanted to thwart or discredit pseudo-Omega, I could base my decision on a source of randomness. This brings me out of reach of any real-world attempt at setting up the Newcomblike problem.

It's not a zero-sum game. Using randomness means pseudo-Omega will guess wrong, so he'll lose, but it doesn't mean that he'll guess you'll one-box, so you don't win. There is no mixed Nash equilibrium. The only Nash equilibrium is to always one-box.