The recipe does not say how much cat food, but it does say every other day, so I think it's a safe assumption that the chickens are not more cat food than the amount of scratch or birdseed.
The scratch grains and birdseed bring the protein content so low that the cat food is just compensating, not pushing it too high.
Why not skip the layer feed and just use chick starter?
The only special thing about layer feed is the amount of calcium. If your hens are not laying, layer has too much calcium. If they are laying, layer has about the right amount of calcium, so adding chick starter means you need to provide oyster shell so the layers can get the extra calcium they need. You can skip the layer feed and just provide chick starter plus oyster shell. That gives you a higher protein content, and lets every hen regulate her own calcium needs with the oyster shell, and you don't have to buy & store an extra bag of stuff (the layer feed.)
Provided separately so the chickens can choose to eat it or ignore it, the rabbit feed is probably safe enough.
Chicken food already has an amount of fiber that works well for chickens. Adding more fiber is not necessarily going to make them healthier. It's kind of like people: there is some amount of fiber that is good. More is better until you reach that level, but adding more past that point is not better.
