I don't have any personal experience with atrophied villi, so this suggestion may not help, but I have done a lot of research on leaky gut issues, and one of the main recommendations that keeps reappearing is to drink lots of bone broth (which contains proline and glycine in the form of gelatin) and supplement with L-Glutamine (an amino acid which is required by the intestines to fuel repair). I've been using homemade bone broth, daily supplementation of L-Glutamine, and a low-fiber diet to heal my digestive issues. It took months, but I was successful.
From the Body Ecology website:
Glutamine is the most important nutrient that you can give to your body to support the repair of the intestinal lining. It is the preferred fuel and nitrogen source for the small intestine. Studies have shown that glutamine supports the regeneration and repair of the intestinal epithelia.
L-Glutamine the villi super healer for coeliacs | Gluten Free Guerrillas community | HealthUnlocked
Healing Gut Permeability: What You Need to Know / All Body Ecology Articles
Broth is Beautiful - Weston A Price Foundation
Gelatin, stress, longevity