That is kinda why I was thinking that this whole "it was an accident" thing is really important to him; for some odd reason. I don't know how you break into a house, sexually assault a defenseless 6 year old child, bash their head in with so much force it's hard to imagine, then choke them to death and call that death an accident. Buuuttt, it's important to him that that notion be conveyed and "understood".
AL, I know you doubt that he did this.
Let's imagine for a moment either way...that he did it, or else that he believes he did it because he's so delusional about the case he believes he was the perp.
The accident thing could be his way of rationalizing what either did happen or he believes happened with him as the perp. Let's stipulate that all of those things you mentioned he did indeed do or thinks he did. Doesn't sound like an accident...or does it?
It might, IF he spins it that when he went there he did not have in his mind to kill her, but that she reacted against him when she realized what was going on and he was just trying to quiet her or subdue her to keep from alerting the family, and that somehow he got out of hand because her reaction against him FORCED him to.
Even the garroting could be explained away if he rationlizes it. That could be explained as his way of "making love to her", sick as it is, but it wasn't meant to kill her. I don't know what spin he'll put on it, but bottom line he could say he admits to everything EXCEPT having the intent to kill.