Nice story, but the title should be “The Thing That Binds You And Me.”
English speakers have been conditioned to shy away from the use of “me” in compounds like this, but it’s easy to figure out the correct pronoun form simply by dropping the other term.
For example, “My mom and ____ went to the mall.” Unless they’re Tarzan of the Apes, a native speaker would never say, “Me went to the mall.” It’s “My mom and I.”
Same here. Unless the person is a Rastafarian, they wouldn’t say, “The thing that binds I.”
Still, a very nice story.