In reply to the 7 "untenables"
I. The nature of Avidya. Avidya must be either real or unreal
This is like asking whether a dream is real or unreal. You can answer both real and unreal. It is real in that it exists as a real illusion. The dreamer is real and the dream is real, but without the dreamer the dream could not exist. So in truth the dream has no reality without the dreamer.
II. The incomprehensibility of Avidya.
All thought is illusion. Thought appears in the dreamer and appears to the dreamer as thoughts of the dream character, but the dreamer is not thinking and nor is the dream character. The dream is simply appearing fully formed in the dreamer. Thought is not to be trusted because it is illusory. Thinking is not knowing, and knowing is not thinking. You are the knowing.
III. The grounds of knowledge of Avidya.
Avidya is not well described as "an obscuring layer which covers Brahman", but it is a fair description. The idea "I am the thinker of thoughts" appears in Brahman, and Brahman is mesmerised with the thought of being the thinker and doer for a time.
Then the daydream of being a thinker and doer ends, and this end of the daydream can SEEM like the lifting of a veil or the removing of a cover. In truth all that happened was that the 'content' appearing in Brahman changed, like it continually does :-)
IV. The locus of Avidya.
There is no locus. Everything is Brahman and Brahman is nowhere. Brahman has no locus. Time and space are concepts appearing in Brahman.
Avidya is a passing appearance in Brahman. There is no such thing as an individual soul. There is only Brahman. The individual soul is just an idea born of the thought "I am the thinker of thoughts". It is a daydream about being the thinker of thoughts and the doer of doing.
V. Avidya's obscuration of the nature of Brahman.
Avidya obscures the nature of Brahman in the same way that a daydream obscures the daydreamers true nature. You may daydream of robbing a bank when your true nature is that you would never ever do such a thing.
Another way is to look at it like this. Sometimes you can be watching a movie and become so engrossed in it that you 'daydream' yourself to be the hero in the movie. When the hero is in danger your own heart beats as if it was you in danger. In this case your daydream has obscured your true nature because you are not a hero, you are just a timid weakling ;-)
The removal of Avidya by Brahma-vidya
It is not the removal of Avidya but it is the end of Avidya in a way.
Consider the analogy of a lucid dream. The dreamer awakens to the dream, and realises that he is asleep on his bed, and that this is a dream. The dream continues but now the dreamer is aware that this is a dream.
Brahma-vidya is like lucid dreaming. The dream continues, but because it is now known to be a dream, the dream is over in a way, because the dream is now a lucid one.
VII. The removal of Avidya.
The removal of bondage refers to the bondage of the dream. Once the dreamer realises that he is dreaming he no longer suffers any of the fears or pains of the dream. This is release from the bondage of suffering.