Aha. That reply is much more informative and shows that you have indeed done a great deal of reading on the matter. Sorry for jumping to conclusions previously but as you say yourself, it wasn’t a well-thought out original reply 
I do not however change my opinion - and it has to be an opinion since no actual research has been done on this yet. Geeta Iyengar is really a chip off the old block. I can’t comment too much as I will admit I have not read “A gem for women” but most of my objections to advice in this area stem from her esteemed father. Toxic may be a bad translation (?) but I think not. I still object. Coming from a woman its even worse - what kind of self-image does that word spring from?
I do own and have read “Light on Yoga”, “Light on Pranayama” and also a lesser know work entitled ?The Tree of Yoga? from which a lot of my objections arise. I quote from this: (italics are mine)
?..it is always advisable to avoid the practice of inverted poses during the menstrual period. The natural flow at the menstrual period is discharge, and if the discharge does not take place properly, you have headaches and have to go to the doctor for treatment. ?. Now, if you do inverted poses at the time of menstruation, [I]there will be a tendency to absorb instead of discharge.[/I] If the discharge is blocked by doing inverted poses [I]this may give certain coatings inside[/I]. To begin with you may not find there is much effect, but as a result of holding the discharge through the effect of gravity, [I]a coating may be formed inside, which may later lead to various diseases including cysts, cancer and so on[/I]?
As I mentioned before the act of lying supine also somewhat prevents the flow from leaving the body, due to the design of the female vagina. This is scientific fact. So, for example, during a nights sleep of say 8 hours or so, the flow (unless substantial) will be ?held? until the woman stands up. Why then does this not cause the claimed ?absorption? and ?blockage? and lead to various diseases yet inverted asana for a few minutes does? It just does not stack up.
As far as the energetic principle of apana goes there is also to consider that apana governs the excretion of faeces and urine, which do contain toxins. So why is it then that inversions disrupt the apana relating to menstruation and not to urination or defecation? Surely if inversions cause ?blockages? to and ?absorptions? of menstrual flow they might similarly cause blockages and absorptions of urine or faces?
I am impressed that you have so widely read of women yoga teachers. If you are truly interested then may I suggest adding Jeannine Parvati Baker to your list? Now she was truly a yogini!
I was very fortunate in my yoga therapy training to be taught by the wonderful Dr Ruth Gilmore PhD, a yoga therapist who is also a lecturer in physiology and anatomy so the practical and scientific was married with the esoteric and spiritual.