What I did with my first manga is pretty similar to your google doc. I would copy every sentence into a document, break apart every word in the sentence and add a definitions / grammar info. That info goes in bullet points right below the sentence. Then I would try to put together a meaning from it all before moving to the next sentence.
Over time, maybe during the second manga I read, after getting a grasp on grammar I felt like literally copying down every definition every time was getting in the way of me remembering words. I wasn’t reading the Japanese when understanding the sentence, I was be putting together the English bits that are my notes into a meaning. So I started to write down less and less definitions and grammar. Nowadays if I can keep enough in my head to understand the sentence only looking at the vocab sheet, I only write down an English translation.
I still write down a fair amount of definitions, but not at a “sentence breakdown” level of defining most every word. Well… unless it’s a hard sentence, which still happens fairly often 
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That’s just what worked for me. I’m sure others have different methods. Everybody has to find what works for them. Just keep asking questions and reading replies in the book club and you’ll find that eventually you’re asking a lot less questions. 
Tagagi-san was my first manga! I can confirm it gets a lot easier, even if it takes a few books to notice a big difference.
I struggle with this too. Sometimes I’ll translate a sentence but not really think the meaning makes sense in a story, then go through the forums to find out that I had the meaning right but wasn’t confident enough to think it actually makes sense in the story. I can’t remember any particular examples now, but this for sure happens when characters make jokes.
Something that I’ve been trying to keep in mind lately: even if this whole manga were in English, I wouldn’t quite understand all the nuance. Who is speaking in that bubble? What exactly does that person mean? Maybe it’s clarified later, maybe it just went over my head, or maybe it’s just unclear. Of course that happens a lot more when reading in Japanese, but I know it will get better over time!
I don’t really have a solid grasp on many sentence ending particles and filler words myself. I think you’re right that it can help with determining a character’s intent. Like the difference between よ and ね (linking to a Tofugu article because I’m probably oversimplifying a lot): either assuming the listener doesn’t or does already know what you mean can have a lot of impact on how forceful something sounds, depending on the situation. Speech styles can help distinguish characters too, which somebody talked about earlier in this thread.
