Try putting a bell on the cats' collars, so you know where they are. Training isn't effective if you can't catch them all the time. Whenever you're not able to watch the cats, keep them out of the room where the birds are. I also know that cats can be very sensitive about surfaces on which they are walking. I remember seeing some kind of electric mat that was used to keep them off the furniture, and it gave some kind of vibration whenever an animal stepped or lied on it. Perhaps that's something you could have on the floor around the cage.
Before I moved out of my mother's house, my Sammy had an encounter with one of her cats...but this one ended poorly for the cat. It's a long story, but I didn't get along with my family, and my sisters thought that if their cat got my bird, it was my problem, not theirs. Well, one time I was laughingly told that Sammy was walking on the floor in the living room, and that if the cat got him, "you'll find a bloody mess." I found Sammy very hyper and chasing one of the cats, and scooped my bird up. He had hairs on his beak. The cat had blood on its tail. The cat never went near Sammy again. And I still don't like cats.
~Chris
Before I moved out of my mother's house, my Sammy had an encounter with one of her cats...but this one ended poorly for the cat. It's a long story, but I didn't get along with my family, and my sisters thought that if their cat got my bird, it was my problem, not theirs. Well, one time I was laughingly told that Sammy was walking on the floor in the living room, and that if the cat got him, "you'll find a bloody mess." I found Sammy very hyper and chasing one of the cats, and scooped my bird up. He had hairs on his beak. The cat had blood on its tail. The cat never went near Sammy again. And I still don't like cats.
~Chris