I’m finding "correct" to be a loaded term here. It is correct in the sense that your conclusions follow from your premises, but in my view it bears only a superficial resemblance to Newcomb’s problem.

I don't care about Newcomb's problem. This post doesn't care about Newcomb's problem. The next step in this line of questioning still doesn't care about Newcomb's problem.

So, please, forget about Newcomb's problem. At some point, way down the line, Newcomb's problem may show up again, but when it does this:

Omega is not defined the way you defined it in Newcomb-like problems and the resulting difference is not trivial.

Will certainly be taken into account. Namely, it is exactly because the difference is not trivial that I went looking for a trivial example.

The reason you find "correct" to be loaded is probably because you are expecting some hidden "Gotcha!" to pop out. There is no gotcha. I am not trying to trick you. I just want an answer to what I thought was a simple question.