(I'm not a native speaker, nor am I a linguist.)
It seems to me that, both ぬ and ざる are used, but there is a difference. They are used for different writing styles. ぬ is used in 和文 while ざる is used in 漢文, as well as constructions borrowed from 漢文. I think that's why ざる appears much more frequently in that passage.
And also, ざる is used to conjugate ず because ず is uninflectable. The same goes for かり adjective. かり and かる are only reserved for conjugation use. You don't use かり to end a sentence or connect two, nor do you use かる to modify a noun.
多かり seems to be an exception, used to avoid the ambiguity of おほし. Similarly, 大きなり is used for the same purpose.
In fact, I wonder if ざる was really used in spoken language when Chinese canons were introduced in Japanese. In fact, it seems to me that the Japanese ancients tended to choose or create expressions that are archaic and stilted even then to render the ancient Chinese counterparts.
As I don't have enough reputation to add a comment, I just write them here.
@snailplane: They will not be confused. They should be はなれ ぬ 故 and はなれ ぬる 故 respectively.
～ぬなり is indeed ambiguous though, but the ambiguity mainly comes from なり. It may either means ～したという or ～ないのだ. So is ～ざるなり, which can mean ～しないのだ or ～しないという.