Central sleep apnoea involves failure to regulate breathing. I have not followed the research much but it would surprise me if there were not insufficient breathing as well as stopping and starting. It needs investigating by medical scientists if it hasn't already happened
The oxygen just isn't transfering to the body even when breathing.
This is an unproven assertion. This is correct for metabolic acidosis, but there is no guarantee its correct here. It might be right, it might be wrong, or it might be right for some patients and not others.
Pragmatic treatment has to be considered separately from theory. I have seen treatments fail on good theory, and succeed on bad theory. Reporting success or failure from a treatment is useful for many patients, asserting unproven theory as fact is not helpful.
A successful treatment does not mean a theory is right. Failed treatment does not mean a theory is wrong. Only proper studies with control groups etc. can lead to reasonable scientific claims being upheld. When something measurably succeeds or fails under controlled conditions you can make stronger inferences.
If the claim is its an oxygen deficiency, then you will need a study in ME patients which measures at least blood oxygen saturation, possibly a full gas analysis, and possibly arterial blood gas measures. Even then you need to be careful about interpretation. Problems in distribution might arise, as microcirculation misregulation could leave places with less oxygen. Problems in distribution of oxygen dumping might arise, as patches of high acidity will induce increased oxygen dumping at that point, leaving less available for other places. Such high acidity patches seem likely in ME, at least some of the time.
I want to restate my caution about interpreting from a symptom. A symptom can have many causes, especially when its vague. In some patients a given hypothesis might be right, but to demonstrate that might be very difficult if it turns out the symptom has many causes. One single cause for a heterogeneous group is very difficult to find, if not impossible. Other ways of looking at things are needed.
I think this symptom grab-bag approach is a big issue in why most of psychiatry and most CFS research has been a let down. Heterogeneous conditions require other methods. To prove a symptom has a single cause is a big ask, but its important to do that if it can be done.