I don’t think you will be able to keep her totally clean. Every cross beak I’ve seen has some food always stuck on its face. I don’t bother with the stuff that’s near my girl’s eyes or really anywhere on her face unless it's easy to wipe off, but there are a couple of things I do that have really helped her cleanliness.
First of all, everyone always suggests a deep bowl for cross beaks, but I find with mash, this guarantees a huge mess all over the head, neck, and chest feathers, and I don't think a deep bowl is necessary for most cross beaks as long as they are not eating dry food. I use a smaller shallow bowl and feed mine 3x a day most days (sometimes I just can’t be home). This is the bowl I use (although the bird in the photo is not my crossbeak, but a sick chicken I separated).
I fill this bowl to the top for my cross beak. I just bought a couple of these at
Wal-Mart - it was the Pioneer Woman brand, mini pie plate. My cross beak's face and upper neck still get messy, but it's so much less than with a deeper bowl.
I understand the frustration with the crop emptying quickly. I also have this problem with my cross beak, although it doesn’t sound as bad as yours. It seems the food just goes right through her; a lot of it looks nearly undigested in her poop.
I bathe my girl about once a week (just the messy parts) using this foamy Vetericyn shampoo:
https://www.amazon.com/gp/product/B01E91NEP8/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
It sprays on and is super watery, lathers up well, and washes out easily. I love it. I spray a bunch on wet feathers and just try to work all the hardened goop out of her feathers. There are usually some spots I just can’t clean, but for the most part, it has worked pretty well for her.
Every time after she eats, I just use warm water and a very soft wash rag to gently wipe out all the food that I can get out of her feathers and then I blow dry her. She’s never completely clean but I can’t shampoo her every meal and I don’t know how good that would be for her skin anyway. Another suggestion is to use a very soft tooth brush to try to gently brush out some of the mess (again after wetting the feathers if they are dry) – I use this kind:
https://www.amazon.com/gp/product/B00N32BB46/ref=oh_aui_search_detailpage?ie=UTF8&psc=1
It helps a little but is definitely no magic solution.
I also just noticed your chicken is only 2 months old. I think things are going to get easier for you as she gets bigger. Hopefully as her crop gets bigger and can hold more food, you won’t need to feed her as often. I also am hoping that as her beak gets adult sized, maybe you don’t have to worry so much about the food getting up her nose. Hang in there!
When I first started really working with my cross beak chicken (which wasn’t until she was 3-4 months old because I didn’t realize how skinny she was), I was spending about 5 hours a day getting her to eat and she still wasn't getting enough food. It took a long time to solve that problem (sounds like you have solved that one too). But then there was another problem and another. As each problem is solved, another comes up until you finally get your rhythm with her and things are good. It seems that most cross beak owners are doing things differently from each other. I have found that a lot of the popular advice for cross beaks just didn’t work at all for mine. I’m sure that if you keep experimenting, you will find a way to make it work.
