I've just managed to read the first article about the pure oxygen breath holds now. A very nice presentation, listing different aspects of the pure O2 apnea. Very interesting topic, and indeed still not sufficiently studied. Likely, there will be no miraculous new explanation of the mystery anyway - the later urge to breath certainly comes as a result of all (or most) of the aspects listed in the article. The studies just need to quantize better their respective contribution. The mental aspect may be perhaps more important than it sounds.
However, I was surprised not seeing two of the most important aspects listed in the article: the Haldane effect and the hyperventilation. Pehaps Sina could add them to the list, so that the article is more complete.
When preparing for an O2 breath-hold, and breathing from a regulator, even if you are not aware that you have to hyperventilate strongly before an O2 breath-hold, you will do it. First of all unconsciously because you are preparing for an unusual performance, and then because when you breath from a regulator, you won't take any shallow breaths, but you will certainly take several full deep breaths, which already represent serious hyperventilation. And if you know something about O2 breath-holds, you'll hyperventilate as much as you can, since unlike at hyperventilating with plain air, it does not represent comparable risk - you risk neither an early BO at the start, nor the reducing of hypoxic tolerance due to the shift of Bohr curve - it is irrelevant at O2 apnea, since you will quit the hold far before the blood starts to desaturate.
And then, even without the subconscious or voluntary hyperventilation, the high ppO2 in lungs leads to faster evacuation of CO2 from the blood, hence already breathing pure O2 without hyperventilating has similar effect anyway.
And that's already related to the second very important factor omitted in the article - the Haldane effect. The Haldane effect is a property of hemoglobin to bind CO2, in relation to the O2 concentration. Simpler told, oxygenated blood has a reduced capacity for binding/carrying carbon dioxide. So when you do an O2 breath-hold, the CO2 produced in tissue is not being bind to the hemoglobin and transported away in the blood in the same level as normally, but in a much reduced way. It stays in a much higher concentration in the tissue where it is produced, and does not reach with the same force the chemoreceptors in the medulla oblongata or in the aortic body. Hence later urge to breath is not really so much surprising as presented in the article.
These two effects alone certainly do not explain everything, but I believe that they are contributing to the delayed urge to breath considerably, and that they should not be left out of a review addressing this topic.