From the OP:

I create a perfect simulation of you, and run it through a thousand simulated years of horrific torture (which will take my hypercomputer all of a billionth of a second to run), after which I delete the simulation and hand you a box with a billion dollars in it.

My interpretation of your interpretation, which you have said is basically right:

And if Omega tells me that he has created n simulations of me which have completely equal experiences that I have had until now, including the dialogue with Omega, I should assume 1/n probability of not being one of those simulations.

So, we have Omega telling the simulations that it is going to give them box with billion dollars (if they choose what they choose) and instead tortures them and then deletes them. This is an explicit lie, isn't it? Moreover, Omega tells the simulations that they would be simulated, but unless Omega can create an infinite regress of simulations of simulations (which I consider obviously impossible), at least some of the simulations aren't simulated in violation of Omega's promise to them.