I will be brief in my reply to your posting, so I will only give but the briefest of replies to what you state above. I have read a large number of books that were written by Arab historians with respect to this particular region.
I am also well aware of the book by Arthur Koestler and of the points he raises in this and I wondered at the time if this was the basis upon which you raised your original posting. That book gives credence to only one popular version of matters, but there were a number of Arabic historians who would equally dispute what is said in this book. The two words, political expediency, were stated by other sources and the "conversion" is also said to have only been of the Khazaric royalty and aristocracy, who wished to appear neutral in the area between those states in that region who espoused Islam and Christianity. There was no such "mass conversion" of the actual Khazar populace and there were over 100,000 Muslims who were never subjected to the stated "mass conversion". Indeed, had this occurred, retribution would have soon been visited upon the Khazar state. Amongst others who were not subjected to such stated "mass conversion" were Khazars who still followed the Greek Orthodox, Nestorian and Zoroastrian beliefs.
The demise of Khazar power was finally commenced in 965AD by the Rus, under the leadership of Sviatoslav, who attacked and destroyed the two major Khazaric citadels of Tamatarkha and Sarkel, before laying waste to their capital city of Atil in 968AD.
I have read books on the Ashkenazi Jews and their history and of their connection to this region.