Siku, I am afraid you do not exactly understand the term hyperventilation. Hyperventilation is ventilating over the metabolic needs of the body. It means that when you ventilate deeply after a physical effort, it is usually not hyperventilation (unless you overdo it). In the same way, when you do your 1:2 breath-up, I bet that you ventilate deeper than you would normally. And if you ventilate deeper, even if it is much slower than the normal flat breathing, you are very likely hyperventilating. And then, reducing the heart-rate during the recovery is counterproductive. During the recovery, you need high heart rate to accelerate the removal of toxins and waste metabolic products from the body, and to improve the oxygenation. Relaxing the muscles and mind will help, but artificially reducing the HR by the stimulation of the vagus nerve will slow down the recovery.
@ run3fun143 - unlike at breath-holding with air, at breath-holding with oxygen, the hyperventilation is necessary - without it you would risk very high hypercapnia (excess CO2 level), and CO2 blackout. Unlike at air breath-holds, hypoxia is not an issue at oxygen breath-hold. Hence oxygen breath-holds have very little common with normal breath-holds.