I think that all you are observing here is that your probability that other agents know the result of the coin flip changes between the two situations. However, others can know the result for either type of flip, so this is not really a qualitative difference. It is a way in which other information about the coin flip matters, other than just whether or not it is logical.
You achieve this by making the coin flip correlated with other facts, which is what you did. (I think made more confusing and veiled by the fact that these facts are within the mind of Omega.)
Omega does not have to have advance knowledge of an indexical coin flip. He just needs knowledge, which he can have.
I think that all you are observing here is that your probability that other agents know the result of the coin flip changes between the two situations. However, others can know the result for either type of flip, so this is not really a qualitative difference. It is a way in which other information about the coin flip matters, other than just whether or not it is logical.
You achieve this by making the coin flip correlated with other facts, which is what you did. (I think made more confusing and veiled by the fact that these facts are within the mind of Omega.)
Omega does not have to have advance knowledge of an indexical coin flip. He just needs knowledge, which he can have.