Hip
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The Bohr effect only applies to oxygen bound to hemoglobin on red blood cells. It does not apply to oxygen which is dissolved in the water component of the blood.
Normally, around 1.4% to 1.9% of the oxygen carried in the blood is dissolved in the water component of the blood; the rest of the oxygen is carried by hemoglobin. So in normal circumstance, hemoglobin carries the vast bulk of your oxygen.
Hyperbaric oxygen therapy (HBOT) uses high ambient pressures of up to 3 atmospheres to dissolve more oxygen into the water component of your blood. HBOT increases the amount of dissolved oxygen by a factor of around 20 times, meaning that with HBOT, up to 30% of the oxygen carried in your blood is oxygen dissolved in the water, and the other 70% is hemoglobin-bound oxygen carried by red blood cells.
In that way, HBOT makes a lot more oxygen available in the tissues.
HBOT does not affect the amount of oxygen attached to hemoglobin, because the hemoglobin is nearly always fully saturated with oxygen, and thus cannot carry any more oxygen than it normally does, even when oxygen supply is plentiful.
HBOT also does not affect the amount of CO2 in your blood, because when you do HBOT, you are breathing normally, not hyperventilating. So the Bohr effect does not really apply to HBOT.
So you would expect that HBOT would deliver much more oxygen to the cells, and thus if a shortage of oxygen at the cellular level were an issue in ME/CFS, then you would expect HBOT to make dramatic improvements to ME/CFS. HBOT does provide some mild benefits for ME/CFS patients (and especially for fibromyalgia patients), see this study, but nothing much more than that.
So the fact that HBOT does not help ME/CFS very much seems to indicate that oxygen shortage is not the issue in ME/CFS.
I don't myself have much problems with PEM from physical exertion (though I do get PEM from mental exertion), and even when my ME/CFS was more severe, and I was very weak physically, and could barely do 5 press-ups, I still did not get any of the lactic acid burning feeling in my muscles. So unfortunately I cannot really get involved in the interesting lactic acid experiments and testing detailed in this thread.
But if you look at the Myhill et al research on the energy metabolism in ME/CFS, they found blockages and impairments in mitochondrial function in ME/CFS — and remember it's in the mitochondria that oxygen is utilized, so an impairment in mitochondrial function would impair oxygen utilization.
Myhill et al then discovered that ME/CFS patients try to compensate for their blocked mitochondria by generating energy by other means. Some ME/CFS patients, like yourself, appear to increase their anaerobic glycolysis in order to generate energy by alternative means, and in these patients, you get the problem of lactic acid build up and lactic acid burn in the muscles. These patients who use anaerobic glycolysis to make up for the energy shortage are known as the Group A ME/CFS patients.
But not all ME/CFS patients use anaerobic glycolysis to make up for their mitochondrial blockages and energy shortfall: the Group B patients likely use the adenylate kinase reaction to generate energy during exercise. In my understanding, these Group B patients will not experience the lactic acid build up.
I think your experiments in using hot / cold exposures to dilate muscle blood vessels and capillaries are interesting; however, my own interpretation of why this blood vessel dilation helps is simply because it washes away the excess lactic acid from your muscles (which then gets converted back to glucose in the liver).
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