So, I think the most important thing is that if the story is known to be fan-fiction, it needs to establish a connection to the characters it's going to use quickly. Otherwise the implied audience (the fandom) might lose interest. I know the use of the word "gremlin" was hinting at that, but I don't think it was strong enough. To that end, I think starting after the main characters have met A-chan and taken an interest in her story would be better. That way you can start with a fan-favorite and establish the main characters at the same time. The other bits can then be woven in as flashbacks, preferably at times where they'll seem relevant to A-chan's story (like a bit in the backstory reminding one of the main characters of their own past). You could also have parts of A-chan's story spark discussion among the main characters that reveals more about them.
Regarding the unimportant bits that you'd like to see mentioned, all you need to do to make them important is make the main characters see something in them. Like, is there something in Magni's parts that one of the main characters can particularly relate to?