Trying to find more on Saigo Tanomo, I did a little checking. Here is a reference I received, unfortunately I do not have a near source or English translation. Perhaps you could give it a quick look (if you haven't already).
"A mainstream Japanese source to consult for Saigo Tanomo, and for many prominent retainers of Edo period domains, is the biographical encyclopedia Sanbyaku Han Kashin Jinmei Jiten.
I have looked at this work. The Aizu han is dealt with at the beginning of Volume 2, pp. 7-112. The biography of Saigo Tanomo occupies just over two columns on pp. 41-42. There is no mention of his education in the Nisshinkan, nor any mention of his learning Onyodo at the hands of Takeda Soemon, who is not listed in the work.