I LOVE her name! It comes from Quetzacoatl, the plumed serpent god, creator of the world and mankind and god of intelligence, science, learning, etc.
Don't use that lamp. It's no good, the Ktemp is way too high. You need to get one that has a CRI as close to 100 as possible (no lower than 93) and a Ktemp between 5000 and 5500 and put it in the ceiling fixture (try Dr. Mercola's FS bulbs).
The gloop stays out all day long along with the raw produce. Look in the diet section and you will find several recipes for gloop but, if I were you, I would start with a simple one made out of only VERY lightly cooked whole grains and no veggies until she starts eating them -then and only then start adding veggies.
Also, I forgot to ask you. Do you have young children or a very busy household? Because grays are stressed out by hullabaloo, they need quiet households. You should take her to the vet but I doubt the problem is physical... with grays, 99.999% of the time, plucking is from stress.