I finally figured out what has been causing Baby E's constant low-grade reaction for the last several weeks. It was the nystatin medicine.
I found out that the people at the compounding pharmacy had not been honest when they kept telling us the liquid in the nystatin suspension was nothing but water.
They were adding things like glycerine and xanthan gum and refusing to disclose that to me or even to my doctor.
Once I got them to admit that, they were claiming that the glycerine was petroleum-derived and the xanthan gum was grown on wheat molasses. Even if that WAS true, which I doubt, the pharmacist verified that the stevia they were using was made via alcohol extraction.
But, also, I found out that a standard method for growing nystatin is to culture the bacteria in a corn meal medium. It can also be grown on a soy/glucose (probably corn sugar) mixture. More details and links to my research here.
Her eczema started to clear up within half a day of taking her off the nystatin, which we had been giving 4 times per day.