I would have waited until you are up, but I am going out later to see a Japanese movie (not something I get to do often, but there is a Japanese film festival on here this week).
So, my thoughts on p61.
Background from previous page: acquiring the Book of Friends would enable power over many youkai.
おかげで Because of that
友人帳を狙ってくる輩もいて there are also those who come after the Book of Friends (i.e. with the aim of taking that power for themselves)
(ニャンコ先生もその一匹）(Nyanko-sensei being one of them)
不本意ながらも 多くの名を預かる身として As the person entrusted with the care of many beings, albeit reluctantly (ie it wasn’t my intention to take on this responsibility)
帳を守る責任もあり、I also have a responsibility to protect the book, and
煩わしいことこの上ない。it is the most troublesome thing. (There is nothing that could be more troublesome.) Or as I’d prefer to translate it: It’s a right royal pain in the butt.
I think you pretty much have this, but I’ll put my translation up so you can compare if you want to.
どこでききつけるのか: I wonder where they hear about it
放めんを求め訪ねてくる者も増えはじめ: The (number of) youkai coming to visit and request their freedom is starting to increase, and
徐々にではあるけれど名を返す日々かつづいている。: although it’s gradual, days when I return a name are a regular occurrence.
I hope that helps.