I do the exact same thing with my puppies, clean bedding (towels or padding) on one side, pee area with newspaper or pads on the other.
But Joker was getting the tar beat out of him so I put him in his own kennel. I put a wash cloth in a small dog food dish and he slept in the dish. I kept a saucer of water, a saucer of milkshake, and a saucer of canned food with a few pieces of dry food too. He also had a pee area, but he is almost houseborke to outside now.
Maybe work on your baby "lapping the formula on her own first thing" When she does this, this will free you from the bottle feedings. "Then you can rest!" Then just always offer a tiny of canned, a few kebbles of dry. If she drinks the formula her self from a cup, then just keep the other food available at all times. She will adapt.
You have to be exhausted. Try having her drink from a cup or saucer, your special formula, in her own special place. Once she does that, just keep all of that she can drink available all the time but also have dry available if she wants it. I think you have it whipped if you teach her to drink on her own.
Joker wanted to eat solids before everyone else too.....he was so hungry. He Had to depend on me....and I just couldnt keep up with his needs as he grew.