We don't need a perfect simulation for the purposes of this problem in the abstract - we just need a situation such that the problem-solver assigns better-than-chance predicting power to the Predictor, and a sufficiently high utility differential between winning and losing.

The "perfect whole brain simulation" is an extreme case which keeps things intuitively clear. I'd argue that any form of simulation which performs better than chance follows the same logic.

The only way to escape the conclusion via simulation is if you know something that Omega doesn't - for example, you might have some secret external factor modify your "source code" and alter your decision after Omega has finished examining you. Beating Omega essentially means that you need to keep your brain-state in such a form that Omega can't deduce that you'll two-box.

As Psychohistorian3 pointed out, the power that you've assigned to Omega predicting accurately is built into the problem. Your estimate of the probability that you will succeed in deception via the aforementioned method or any other is fixed by the problem.

In the real world, you are free to assign whatever probability you want to your ability to deceive Omega's predictive mechanisms, which is why this problem is counter intuitive.