Particularly in this case where Omega is being explicitly dishonest - Omega is claiming to be either be sufficiently omniscient to predict my actions, or insufficiently omniscient to predict the result of a 'fair' coin, except that the 'fair' coin is explicitly predetermined to always give the same result

Coin is not predetermined, and it doesn't matter if Omega has hand-selected every result of the coin toss, as long as we don't have any reason to slide the probability of the result to either direction.