Ok, I have advice for you from two different angles, just based on what I've seen other people do in the past. We personally did not have this issue, as Tucker had a g tube and therefore his formula was always covered (or we were just lucky!).
First: in our area, all babies still on any formula past age one are urged to switch to "big kid" formula. Some parents hear it from pediatricians, some from GI, Tucker's surgeon is the one who switched him to Pediasure at one year old adjusted. It is something I did not even think about, I thought he could get the infant kind until he started eating, but the older kid formula has way more calories, so I get that.
Because there are so many toddlers out there who need the formula, I think it's awful that insurance doesn't cover it without a g-tube. There are many little ones like Charlie, who have feeding issues but have thankfully not needed a tube. My first suggestion would be to appeal the insurance's decision as many times and as often as possible. Does she have a medical case manager? If you have that with the insurance company, they are very helpful in proving medical necessity for things that the company generally refuses right away.
Secondly, a fellow Share mom introduced me to the blended diet when Tucker was almost 4. He had been on 100% pediatric formula since age 1, and he was not really growing. She suggested that we blend up real food (veggies, fruits, milk, etc.) and feed him that in order to help his nutrition. It took a while and some tweaking the recipe to get the calories right, but once we did it really helped him to grow. Of course, he didn't have to taste it, so I never worried about the taste. There are many kids who drink the blended food through a bottle (this fellow Share mom's daughter included-she thankfully never needed a tube either) and love the taste. I could put you in contact with her, that saved us from using a lot of formula because Tucker had 3 blended meals per day, and two cans of formula at school. So it's just another way to go, of course check with Charlie's doctor first to see if she has any food insensitivity or allergies.
I am sorry that I don't have any resources for you that offer discounted or free formula, I know several families who pay a lot of money for it. How soon do you think she'll get on the Medicaid waiver? just curious, as Tucker is 8 and still on the waiting list here in Louisiana.