Q: How can we be said to be conscious during deep sleep when we are not aware of anything?
A: Consciousness is not defined in opposition to ignorance or unconsciousness; but rather it is found fully present in all states that are seen as conscious or unconscious or as any mixture of the two.
That's why there is no lack of reality or consciousness in the state of deep sleep, which is seen as 'empty' and 'unconscious'. It's only seeming objects that are missing in deep sleep. That is the state in which there is no 'consciousness of objects'. The so-called 'unconsciousness' there is not just 'unconsciousness', but rather it is an 'unconsciousness of objects'. That is an objectless consciousness -- unmixed with any object which is taken to be different from it.
Accordingly, although we take deep sleep to be an 'empty' and 'unconscious' state, it is not truly so. Instead, it is that state in which all reality is present by itself -- known fully and directly as pure consciousness, whose very being is to know. No mixture or confusion there appears, to complicate the plain identity of that which is and that which knows. That is pure non-duality.
In dream and waking, that simple non-duality appears in a mixed-up sort of way -- as a relative existence of limited objects that are partially known by consciousness. Thus there appear the relative existences of various different objects, and the partial knowing acts that we call 'consciousness of objects'.
In short, variety is produced by the confusions of appearance, which get superimposed on that which is unmixed and non-dual. In deep sleep, those confusions are removed, showing only the unmixed reality of consciousness that is fully present in what's taken to be real or unreal, conscious or unconscious.
Q: Where does the 'kAraNa sharIra' ('causal' body) fit into this?
A: Shri Atmananda would quite agree that suShupti *avasthA*, as the *state of* deep sleep is in the phenomenal realm of personality. The truth called 'turIya' is not a state. But, in the state of deep sleep, that truth is found shining all alone -- as that self which only knows, whose knowing is its very being -- with no appearances to distract attention away from it.
The kAraNa sharIra is one of those distracting appearances. It is not truly present in deep sleep, but is only superimposed on deep sleep by confused conception in the waking or dreaming mind. The kAraNa sharIra is quite simply the 'unconscious' depth of mind, at the integrating level of the Ananda-maya kosha. It is that mental function which is needed to put together mind's essentially fragmented acts of limited and partial conception. We think of this 'unconscious' depth, in waking and in dreams, to explain how it is that our minds seem able to co-ordinate their thoughts and feelings and perceptions.
In short, the kAraNa sharIra is an explanation in the realm of conceiving mind, and thus to be distinguished from Atma or true self. The kAraNa sharIra is a mere conception of the mind, appearing only in the waking and dream states. It does not appear in the deep sleep state -- where there are no appearances, but only truth or Atma in itself. In fact, it's only from that truth that all co-ordination comes.
The 'unconscious' kAraNa-sharIra is just an inexplicable explanation, which must dissolve completely in the actual experience of deep sleep. In that experience, there can remain no sense of any changing state. All that remains is unmixed self that shines in its own glory, as it always is -- quite unaffected underneath all seeming changes of apparent states. That self is what the Mandukya Upanishad calls 'turIya'.
When yogi's speak of 'turIya' as a nirvikalpa-samAdhi state that comes and goes, they are not speaking of the same 'turIya' as the Mandukya Upanishad. The Mandukya 'turIya' is the changeless self that utterly dissolves whatever comes to it -- including the seeming 'unconsciousness' of deep sleep and also the seeming 'consciousness of objects' in the waking state. As it is neatly put in your quotation and translation from the concluding stanza of the Cangadeva Pasashti:
nideparaute nidaijaNe jAgR^iti giLonI jAgaNe is the true Being. [THAT is the sleep beyond this sleep; which swallows (transcends) this waking too.]
Here, I would interpret 'this sleep' as the seemingly unconscious state which deep sleeps appears to be when viewed from the outside. And 'THAT is the sleep' would refer to the actual experience in deep sleep, where the outside view has dissolved in that inmost self whose changeless shining is there found unmixed. That same changeless shining stays on ever-present in the dream and waking states, utterly dissolving each appearance that our dreaming minds or our waking senses bring to it.
Q: But I do not remember deep sleep - it is a complete unknown.
A: Why is this a problem? It's only a problem if one insists on knowing through memory, or in other words through mind. This is a characteristic problem of the idealist position. To insist on staying in the realm of ideas, on standing in the mind, while looking for a truth beyond.
The whole point of considering deep sleep is that it points to an immediate experience that cannot be remembered from the past. That immediate experience is one's own identity -- just what one truly is, beneath all seeming mind -- in the present. It most certainly is 'unknown' to mind, and so the mind makes a 'big' deal of it, and gives it grand names like 'everything' or 'all' or 'brahman'. But that 'bigness' too is a mental superimposition that gives a false impression. Hence the corrective of deep sleep, where 'small' and 'big' and such qualities are utterly dissolved.