math ace...
I'm glad your hen seems to be making progress although it sounds as though she may have sour crop. The squishy crop is generally a sign. There may not be any sour smell until the feed in her crop has soured. The important thing is for the bird to have nutrition. I can't say about the cat food although I think I had read somewhere that cat food and dog food are not good for chickens. Anyway, if she's pooping, that's a good thing as it means she is getting some food through from her crop and she is getting some nutrition.
I've had a hen who suffered with sour crop for several weeks until I finally found out that any kind of grass caused her crop to be unable to empty properly. It should empty overnight so that it feels flat in the mornings. So, that being said, if you can isolate this bird so that you can observe her poop and monitor her eating. Do not give her any pellets or hard food of any kind. Instead, offer her scrambled eggs (as you have done) and applesauce. Baby food is also good. Mine seemed to like the ham and gravy! Anyway, offer her food several times a day if you can to see if she'll eat.
If she is not eating, you will need to get a feeding tube so that you can get something into her and it is also helpful to use the feeding tube to "flush" the crop. A size 12 french is the size you will need. Put the feeding tube on the outside of her body, beside the hen's neck and put a mark with a sharpie or permanent marker of some kind so that you will know when you have inserted it far enough. To insert the feeding tube into the crop, hold the hen in your lap and use your index finger to pull up on her beak to open her mouth. As you see her tongue, put the feeding tube on top of her tongue and slowly feed it down her throat into her crop. When her get to the mark you made on the tube, you know you have it in far enough. Fill a 60 cc syringe with water. Attach the feeding tube to the 60cc syringe and slowly push the plunger to get the 60cc of water into the crop. Massage the crop. Hold the hen upside down so that she cannot lift her head up. If she lifts her head up, the liquid coming out will pool in her mouth and she will aspirate it and could die. You must keep her head from lifting up. Massage the crop while she is upside down to get as much of the liquid out as you can. By the time you get to the end, you should see whatever is causing the problem...grass, feathers, etc...coming out of her mouth. If nothing comes out, do the 60 cc water into the crop again. I have done it as many as 5 times during a "session" to get out the junk. Once you feel you have gotten everything out, let her rest with no food or water for 2-3 hours. Then, offer her only soft food...no pellets or chicken feed, etc. She will need to be on the soft food for a couple of days once she starts eating. If she doesn't eat, then dilute some baby food with water in a 3:1 ratio with the baby food being the most and use the feeding tube to get it into her crop. You'll need to feed her like this every 4-5 hours during the daytime until she starts eating on her own.
Once she starts eating the soft food and can do that eagerly at each feeding, then begin adding a few crumbles to the soft food to get her adjusted back to regular food. This whole process will take 4-5 days so be prepared.
If this doesn't make any sense to you, let me know. PM me if you have specific questions. I can say that everytime I see my little hen who had such a hard time with this, I am totally delighted that she survived. I had this hen inside my house several times. I would get her "fixed up" and then, boom, her crop would fill after a couple of days. I was at my wit's end until I finally figured out that she could not have even one blade of grass. Once I took her off all grass, she has been just fine. If you can get your hen fixed up this time, try to figure out what caused her problem. If you see a lot of grass coming out as you cause her to vomit, that may be her problem, too.
One additional thing I would mention here. I did the crop surgery on my little hen, too. It only helped for the moment so I would not recommend doing the surgery. I learned that by flushing out her crop, she would get better. I only kick myself for not realizing it was the grass all along. I could've prevented her a lot of misery and prevented my misery, too.
I hope this helps and you can get her back. If anyone reading this topic has a bird with sour crop and you want more info, please PM me. Believe me, I've been there and I'd surely be glad to help anyone who needs assistance on this. These birds can be saved.