Do you agree that Omega declaring its prediction is not what causes me to give it $5, and that making such predictions does not make the subject a money pump?

Yep. This isn't counterfactual mugging and isn't intended to be. The point in this post will apply to counterfactual mugging, but the information in this post will not turn the subject into a money pump.

I see where this is going, and you are ignoring the conventional implicit "All else being equal".

I didn't ignore it. I made this point in the post:

A possible objection to the scenario is that the prediction itself is impossible to make. If Omega is a perfect predictor it follows that it would never make an impossible prediction and the prediction "you will give Omega $5" is impossible. This is invalid, however, as long as you can think of at least one scenario where you have a good reason to give Omega $5. Omega would show up in that scenario and ask for $5.

If this scenario includes a long argument about why you should give it $5, so be it. If it means Omega gives you $10 in return, so be it. But it doesn't matter for the sake of the question. It matters for the answer, but the question doesn't need to include these details because the underlying problem is still the same. Omega made a prediction and now you need to act. All of the excuses and whining and arguing will eventually end with you handing Omega $5. Omega's prediction will have included all of this bickering.

The expected response to this post is, "Well, yeah."