Some further observations:
1) Carotid sinus instantaneous death in humans is a controversial topic and one which has never (to date) been reliably demonstrated to be true.
2) Even if true, the mechanism for death in this sort of manner would have nothing to do with the starvation of oxygenated blood to the brain - rather, the cause of death would be cardiac arrest. And I'd contend that in most cases, a forensic autopsy would be able to determine the difference.
3) Even if this case did involve carotid sinus instantaneous death (and there's no reliable evidence that such a manner of human death even exists in any event), we're still stuck with the problems around this man's claimed story. Remember, he claimed to have wandered off to have a shower once their sexual activity had concluded. and then only chanced upon Millane's dead body some time later. But IF Millane really had died more-or-less instantaneously from carotid sinus stimulation, then we're supposed to believe that the following sequence of events unfolded: 1) the man put his hand(s) to the conscious-and-consenting Millane's neck and started to choke her; 2) Millane died almost instantaneously (and by definition of course, she fell limp, unresponsive, uncommunicative, eyes-closed, and NOT BREATHING); 3) the man somehow a) didn't observe that this had even happened, b) decided (unilaterally of course) that the sexual activity had finished; c) removed his choke hold from Millane's neck; and d) got up and walked to the shower, without a shred of concern that Millane had not moved, communicated, opened her eyes or even breathed* while he was removing his choke grip and walking away. Not credible, IMO. If however the man had claimed that he started choking Millane, realised quickly that she'd gone limp and stopped breathing, and then went in to a panic etc, then his story would have carried more credibility. But that was not his story. QED (once again).....
3) The matter of whether a ligature or a hand was used for constriction is only of minor relevance. One difference is that the use of a ligature looped around the entire neck would necessarily include constriction of the trachea (windpipe) which would obviously have a consequent effect upon breathing - whereas it's possible (and in fact desirable where erotic asphyxiation is concerned) for a choke grip to constrict one or both of the carotid arteries without putting any pressure onto the trachea. Nevertheless, in many instances of erotic asphyxiation, especially auto-erotic-asphyxiation, ligatures are the means employed (for obvious reasons in the case of auto-erotic-asphyxiation....).
4) Even though certain other details that were not included in this man's trial have now been revealed, and even though these new details only tend to paint this man in an extremely poor light, it's important to remember that the Millane case should only be considered with respect to evidence actually admitted into the trial (that is of cpirse to say the judicial/legal case against him, rather than any debate about his factual guilt). But in any event, I'd very strongly argue that, based only on the evidence introduced into the trial, there's sufficient reason to find for murder BARD.
* If a man is in such proximity to, and in such intimate contact with, a woman (which must be the case if he's choking her...), then I'd argue that it would be near-impossible for such a man NOT to notice that the woman has stopped breathing.
ETA: It's certainly possible to determine death by a long constriction of the carotid artery (or arteries), because the manner of death is cumulative brain death. And it's possible to observe this at autopsy because widespread apoptosis (cell death) would have taken place throughout the brain. So the presence of such evidence would effectively prove the cause of death as apoxic brain death, via extended choking. Only in the absence of such evidence could one even begin to consider things such as sudden death through any mechanism.
