(The fact that "it also means “tissue paper” in Japanese (鼻紙)" is irrelevant; homophones are common in Japanese.)
The choice of words is also kind of weird. "Oribana" would work, but that already refers to flowers made of origami. I would have gone with "hanaori" instead. "Hanagami" sounds like you're making paper out of flowers, or flower printed paper.
I have consulted friends in Japan (native Japanese speakers), and even Robert Lang gave me the same comment. It is not my intention to cause controversy with the choice of words, but even the Japan Origami Academic Society would not respond to my request for clarification, so I think this is where a :shrug emoji would go.
You are right in that they are difficult to fold, but not because of the size of petals (I fold models no bigger than from a 1cm x 1cm square cut from the petal), but because of the curvature of the petals that makes it difficult to press and work with.
