"That is what I am suggesting. But none of these translations you provided state that the soul is your brain...."
And Yehowah God formed manof the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
It in now way says that we received a soul, we are a soul = entire body with the breath of life, to kick start it and to continue living.
I'll suggest, what you consider to be your soul, is your memory bank = from the brain, part of the living soul. On death, that memory bank shuts down , goes to sleep as the Bible puts it.