Further our “singular conscious” is an illusion. People with various types of physical brain damage have had their awareness “split” and had something akin to two different consciouses in their brain. Even for “normal” people there are independent processes running in our brain. Our consciousness is in charge sort of the way the teacher is in charge of the nursey school. It might decide when recess is but it can’t stop that one kid from just singing for no reason.

Also to your point I think that if we could transplant a head we’d find that our sentience involves more than the brain. I think we underestimate how connected all of our systems are.