M'aiq is not proof, nor canon.
M'aiq is Bethesda poking fun at us.
If anything, he may be an aspect of Herma Mora with a jester hat on.
When it comes to ancient thinking, the soul is the blood.
There is some evidence of a mind travelling with a soul inside a soul gem unto a new body (Mere-Glim in Lord of Souls)
But there is no evidence of a mind actually being a soul.
That would open up a whole can of philosophical worms.
No, not the in-game M'Aiq the liar, I mean the forum poster whose nick is "M'Aiq", who posted this a page ago in this thread:
There's a difference between conflicting accounts/removal of game-play mechanics and inserting a new bit of lore, though. The experience of being in a soulgem is completely new and there's not a single thing to refute it - that's the thing. There's even an additional (if easter-eggy) account of surviving a soultrap just fine, which I posted before.
About it being 'living'; well, he still had his own identity, the ability to use magic and his ordinary visual shape, so presumably you do actually live as usual in there. But the standard of living are obviously pathetic and not something to aim for. And there's no telling what happens when being used for an enchantment.
As for your theory, I see it more like your soul always being immortal, but it's your body that makes the individual. I think the reason to why he needed new souls to bolster his own is that when in a soulgem or an enchantment, your soul slowly slips away into the Dreamsleeve. The "amount" of soul you have is what's important, not "whose soul" it is. if you refill your body with somebody else's soul, you'll still be you, because it's the body that makes you you. At least that's the conclusion I can draw from the dude in the soulgem being the same guy as he was before. He seemed to remember everything he'd done on the outside of the soulgem, the process of getting in there, even though he had used up I-don't-know-how-many other souls to keep "alive". But it's obviously speculation.
Prince A'tor was soul-trapped, and they attempted to release him into (a new? his original?) body (Redguard). Mere-Glim was also soul-trapped and released into a new body (Lord of Souls).
Again, if you can be soul-trapped, that is, removed from your physical body (which is presumably dead at that point), including your physical brain (which presumably needs a beating heart to keep the thinky-bits running), and still have full access to your consciousness, your memories, your emotions, your personality, then that IS your mind, and as you are nothing but a soul, then that means the mind resides in the soul.