I've also played with the theory, whilst not completely 'catatonic' (I'm not a psychologist and but can't come up with a better metaphor), events happened which were not controllable out of his normal mental state.
Whilst he maintains, when presented evidence, he 'only' committed one (technically two) acts of death by strangulation, is it implausible that he simply doesn't remember the complete horrific acts to his daughters at the time, or of his wife and baby boy? He simply switched off?
Is there a 'revelation' moment when all of a sudden you realise you are the perpetrator of these horrfic acts against your own family?
Could you lie so well because that's what you believe yourself?
If so, the moment of truth would hit you like a brick to understand the enormity of your actions, at some point.
Rambling, just a thought....
Not necessarily my final theory but a thought in my head. Late, tired and foggy. Zzzzzz