I have used Super Glue on a bird toe nail torn too short also on a horse that received a clean straight cut on her side worked great .
Some times the splits can be caused from being dry then a big dose of water repeated a few times from what I read the cells gorge on the water and expand too fast .. I have tried the glue on a plant leaf it did not stay put .
I used a paper based tape, generally used to tape wound dressings so the skin of humans, with great success on the underside of the leafs. What surprised me is that even after more than 1.5 years the tape is still attached to the leaf, even after been wet for multiple times. Doesn't look like it's coming off any time soon by itself.