She learned kanji in school and knows more than most Japanese, who were taught a shorter list
Well, I know you meant no offense for Japanese people, but I want to object to it. I can
easily identify all those kanji you listed, and it's obvious that most Japanese people can read family or location names such like 陸奥, 磐城 or 会津 correctly. (Incidentally, 陸奥 indeed
can read みちのく, as you wrote, but it's also obvious that みちのく is
not used for a family name.) If
she was stumped by a good deal of it, it can't be said that
she knows more than most Japanese. Indeed some names have multiple readings like Osada and Nagata for 長田, but these names are both not uncommon. It's easy to get these two reading.
I've never heard 渠會倍, and I couldn't read it because this name doesn't exist anymore, but I can get the correct reading by googling it. I initially read 久努 as Kudo. In fact, there was Kudo village in Shizuoka prefecture. It has nothing to do with Abe clan, though. Anyway, I can finally get the correct reading Kunu. I believe it's easy for Japanese people to identify each kanji in printed font, and it's not so difficult to get the correct reading just by searching it in internet or printed books in Japanese.
I'm Japanese, by the way.
By 'silent' I meant only that 'yama' is not part of the name as spoken.
The point is that 嶋 is
a single kanji, and not "山 + 鳥". 山 is just a component of 嶋, as Majestic-san pointed out. 山 has nothing to do with the reading of 嶋, as same as 土 for 城 or 木 for 柴. You
shouldn't think these are "compound characters" or something, which is no doubt the key of your misunderstanding about the interpretation of kanji, and the cause of your confusion, I think.
Some kanji, which are called
形声文字 "keiseimoji", were indeed originally made by this method, but it's in ancient period. No one can make new characters anymore. Thus, you don't need to pay attention to the difference between sanzui and sanzukuri in 渠 because the upper left component of this kanji must be sanzui, whether or not it looks closer to sanzukuri to your eyes. In the first place, sanzukuri is never used in this position, as I already pointed out.
I have to look up the correct terminology for the distinction in compound characters between parts that tell you what it means and parts that tell you how it sounds.
Try to search about 意符 and 音符.