So I did the next step. I covered her eyes because the eyes on these dolls tend to fade and I'm not sure if it is because of sun exposure. I then wrapped her face in gauze to keep the cotton balls intact.
I covered her with a sheet and left only the part of her face exposed with benzoil peroxide. I put her out in the sun for an hour.
She came out perfect. Her vinyl was very soft at first but then firmed back up. I know this technique is probably old news for most seasoned doll collectors but it's nice to see that it works.