This was clearly a storytelling experiment, which I'm all for in a creative sense. I don't know if the double suicide metaphor really worked here, though. I had to read it a few times to get what was going on, and when I took the double suicide out of the picture, it gave me a clearer understanding.
Basically, to me, this seems like a "Character A feels unworthy of Character B's love, even though there is mutual attraction" situation. The author even says that Misaki's feelings towards Kokoro are an "incomprehensible existence." Misaki, at first, is confused about her feelings but is actually in denial about the fact that she's in love. When she finally realizes her feelings, she feels inadequate. Kokoro takes the initiative by writing a love song dedicated to Misaki. Misaki rebuffs it (probably as a defense mechanism), but Kokoro counters it by literally writing it down. Misaki reads what Kokoro wrote, and, touched and inspired, she reciprocates but tells Kokoro she doesn't feel worthy of her. Still, Kokoro insists that she genuinely loves her, and Misaki feels willing to try. The double suicide metaphor at the end then becomes a "Characters A and B both are in love and have found something they're both willing to nurture and work on together, which is their relationship."
That's what I got from it, anyway.