If antimatter is moving backwards in time, and the direction of time is defined as the direction in which the total entropy of a system increases, then does that mean that entropy is always at a constant value when considering all the matter and antimatter in the universe?

E.g., let's say all matter starts at a high level of organization and proceeds through time to a heat death. (I have no idea how physics explains the high level of organization at the start of time, but it seems to me that the Second Law of Thermodynamics requires that assumption.) Let's also say that all antimatter starts at a high level of organization and proceeds through time to a heat death. Then, at the very start of our universe, all the antimatter should be at maximum entropy (because that was actually the end of its time). And, at the end of our universe, all the antimatter should be at maximum organization (because that was the start of its time and therefore its time of least entropy). If this is so, then at any moment in time, wouldn't the entropy/organization of the antimatter be balanced by the organization/entropy of the matter?

Is it possible that we have such a small amount of antimatter in our universe right now because we're seeing it at its maximum entropy (already converted into heat energy) and we'll see more of it as we proceed through time?

Additionally, if two equal parts of matter and antimatter annihilate into a burst of pure energy gamma rays, wouldn't this itself be an instant increase in entropy, no matter where in the individual particle's timeline you were and what direction in time the individual particle was moving? So, if you can increase the entropy of a piece of antimatter by annihilating it with matter, doesn't this itself suggest that the flow towards entropy is not what determines the direction of time?