unity of consciousness... [does] actually exist,

The point of my earlier comment about touching a hot plate (ETA: link) was that once you know that your brain is capable of that kind of fiddling, you ought to be convinced of the essential unreliability of all subjective experiences up to and including unity of consciousness. Like the temporal order of events during a burn, unity of consciousness may not be what it subjectively appears to be, so you don't get to take it as a premise.