I feel for you. I have a cat who has driven me insane with this. My cat Beep, who is 12 now, the first few years we had her, she slept in the bathroom at night. I had a comfy bed and her litter box, and she was quite comfy. She loved curling up on the bathroom rug too. Yes, she did paw at the door for a while, but she did give in eventually. But at first, we had to put one of those cheap box fans, that are really loud, we put it near our bed so that we didn't hear her howling and scratching. It did get better. Once she knew the routine, that it was going to happen, she would give up faster.
One thing I saw on Jackson Galaxy's "My Cat from ****", he got an aerosol can that sprays just air, and it makes a kind of loud "psst" sound as it sprays, AND it was motion activated. He put it next to the door and as the cat approached the closed door, the can would go off, and the cat would back off. I don't know where you find such a can, but I'm sure if you google it, you can find one. Something similar that worked for me, my cat is terrified of the vacuum cleaner, and just keeping it right outside the door keeps her far away. We also have one of those air cleaners, the kind with a hepa filter, and it's pretty loud, and the cat doesn't like that either, so keeping that right by the door, keeps her away. You could try that.
You probably are not doing your cat any favors by keeping dry food out all day long. There is no need for that, it it will only lead to obesity which leads to all sorts of problems. We get up super early too, so our cats eat at 5:30 am, and at 4:00 pm, but they also get a bedtime snack around 9-10 pm. If you make that night time meal one of the bigger meals, she might sleep better, with a nice full gut. If she's been snacking all day long on the dry, she will be more likely to gobble down that large meal and then, like most cats, hopefully go curl up and go into a cat coma of sleep. This works for my most annoying cat, who is otherwise a party animal at night. Cats don't need to have food at their disposal 24/7, even though they will tell you otherwise, yes, they will STRONGLY protest and lead you to believe they are going to DIE without a bowl of food available whenever. But establishing mealtimes will give make it easier for you to get your cat on some sort of routine.
She is probably going to protest, scratch, cry, howl, and raise a huge ruckus if you do put her up, in a closed bedroom or bathroom at night, but if you do it regularly, and you do the bedtime meal, and you have the playtime with her in the evening to get some of that energy out of her, she will probably get better.
Good luck. I know what a pain it is to have a cat like this. We don't have to lock our little pain up anymore. She is 12 now, and now and then she will walk into our room at 3 am, crying loudly for us to get up, but if I completely ignore her, she will stop. That was another thing Jackson Galaxy said about this, is that ignoring them is the best thing you can do to to break them of this, and the worst thing you can do is chase after them, yell for them to stop, spray them with water, all of that will just make it worse.