How about getting a cage that is attatched to a very sturdy stand, one that won't tip over?

Putting something unpleasent around the cage is a good idea too.

Can you move the cage to another room where the cats can not access it? Especially at night or when no one is home to supervise?

This may be *part* (I don't think it's the full reason but I'm sure it doesn't help one bit) of the reason why your baby bird is still about bald. Thats a LOT of stress for any bird, but especially one that young. I think putting the cage somewhere out of your cats view is the best idea, the cat will not be able to stress the birds out. Even if you can just movew the cage at night & close the birds in a room that the cat can not get into.