Update: I bought a couple TINY pieces of leather coral (not lobophyton) (also I bought a pretty baby bubble coral for myself) to see how they would do in my tank and if Saint Kyoko would eat them, since I've read about them eating a few other species, but it doesn't seem interested. One of the corals died, or at least I think it did. It was all shriveled, and I removed it. At one point I held the coral directly in front of Kyoko and it seemed more interested in my thumb. I've seen Kyoko slither past the still-living piece without a care. I don't know if they're just not hungry or if they really can't eat that kind...
