First, let's be clear. Science has not solved all the mysteries of the brain.
That being said, there are things that we do know. When you ask, "Where would the unified subject self exist?", are you rejecting the notion that the unified subject self resides in the tissues of the brain; that it is the integrated, interconnected structures of the brain that give rise to the characteristic of a unified subject self? If damage to various locations of the central nervous system can cause corresponding damage to the unified subject self(alter sense of self; e.g. mood, self control, critical thinking skills, language), then it seems most probable that it is this whole integrated system that creates what you term the unified subject self. Sense of self is not the product of one region or location in the brain, but a product of the different regions working in concert.
This unified subject self should not be considered unique to homo sapiens either. Homo Sapiens are at one end of a wide spectrum central nervous system functionality.
I am also curious about your question, "How much information can memory store if it is physical?" Your question implies that there is not enough material/matter in the brain to store a lifetimes worth of memory and information.
If you compare the relative size of mammalian brain structures, we human beings have extra grey matter that more than adequately explains our greater cognitive abilities. And given that we cannot recall every experience in full detail, or have photographic memories of all information we have ever been exposed to, seems to indicate physical limitations to storage, not access to a limitless, non-physical storage system or soul.