Thanks, Heroic. I've kept up on the Stress Coat and that split started to heal. Since then, he's shredded his tail pretty good.
This morning, I was doing a 100% water change, and while I was scrubbing his "cave," I found that it has sharp edges on the inside where he couldn't avoid rubbing against them. I also found that his silk plant has a sharp plastic stem with a point on it. So I gave him a small plant pot instead and replaced the plastic plant with some new live plants.
So now he doesn't have anything that he can tear his fins on (I hope!) and I'm hoping that clean, warm water and Stress Coat will help him heal.