I was LIED to about Library Cards (what you’ll read next is so sad you’ll be SHOCKED)

I moved to Tokyo for school a month ago and so far it's been really great. A very nerdy thing I started to do is collecting all the library cards from each of the 23 wards. Not only does this allow me to access vast swathes of physical knowledge throughout the city, but it's a really great way to explore areas I wouldn't necessarily have thought to go to on my own volition. Not to mention a lot of them are really cute (love the Minato sea otter)! Anyway, I just ran into a snag in my plan. Today I went to Koto to get their library card, but when I went to register, Uh oh! I got hit with "Sorry only people who live/work in Koto, or who live in a neighboring ward, can register for a Koto Library card". This is frustrating because I do go to SCHOOL in a neighboring ward.

I should mention that my interest in obtaining the library cards stemmed from a post made on the r/japanlife subreddit 5 years ago (Here is the link). In this post, OP claims that you can obtain a card regardless of where you live in the city, contrary to the information I was just given. When I first read this I was skeptical but nothing I found showed anything contradictory. Up to this point, since I have around 5 cards, I had no reason to believe this wasn't the case.

Am I screwed? Is this the end? I don't know how many other wards do it like Koto, does anyone know if their ward does something similar? Is there a loophole for me to go back and register for a Koto card anyway? Help!

Also let me know if you are/have done something similar to what I'm doing. It's honestly really fun and it's a great way to practice my Japanese speaking and writing!