Sharing: I've been given math classes for a long time, so what I'll say is only my own experience.
That "redundancy" you speaks of is as relative as it can possibly be. I'm researching for this exact situation because my work now have to do with the elaboration of materials for students to work basically alone, for themselves, at home, with minimal interaction with tutors. And the answer so far is: there's no perfect way to elaborate any materials like that. There's no perfection in writing something that it will, 100% sure, be satisfactory to every reader. It may be never enough.
In this case, I'm just like you. I have this need for detail, give the maximum number of information that is possible to make the reader understand every little thing about the demonstration.
What isn't written anywhere is that when we "give" someone an answer for a problem, we give "our" experience with that exact problem, the way "we" saw it. And what the reader will do with that answer is HIS problem, isn't part of the solution that we proposed.
Many times my friends ask me: there's any way to resume it, to make it simple?
My answer is always: if you understand the answer, you can write it with your own words, put anything that you judge necessary and take off everything you judge that is too much.
But keep one thing in mind: you maybe never be able to know exactly what the person - the one that is asking the question - have on their baggage. So, always put the maximum information that you can, for the good sake of the answer. And when and if someone says it's pedantic, just ignore that, because he probably understood your answer and, in this situation, he fells able to rewrite more efficiently. It means that you have succeeded in this answer, it means a full victory.
That's my point of view, obviously... I remember using a textbook where the autor used to say "the proof is obvious" and skip to the next part, and it always made me feel so stupid for not seeing the "obvious" part. Today I make my own way through the "obvious" and rewrite anything that I judge that need more explanation, and my friends always want my notebooks for further instruction. I'm at some point that I can never throw away an old notebook because there's always someone that needs my notes. And they are always welcome, because math isn't easy anyway, and if I can help, I fell completely honored.
As for my students, I always ask for them to put the maximum information possible, and if they don't know exactly how to say something, that they should describe it with his own words, the best way they can, because with this material and if the answer went through a good place, we can use it and discuss in the class. I've been paying my price. My students sometimes put some long answers, some big text trying to proof their points. So the work reviewing my students classwork is huge... But I like it, and most of the time they understood the basics of it, so I have work to do at the class with them, time to polish the knowledge they have and make them feel comfortable with themselves when writing in math.
That's it. Sorry for the long outburst.