Agree with E!! A GF diet for my daughter saw her gain, and me lose. I also cook with healthy fats, like avocado oil and coconut oil, and both of those have put lbs on her, but taken then off me.
And I still use butter sometimes; I like to use things with flavour. We also avoid sugar...because I just think it has no benefit for any of us. My DD was also FTT and now hovers between the 15%-20%. It keeps increasing though, just slowly. She was diagnosed last year with celiac`s so it is a process. But she was 17lbs at 18months old, and now she is 27(!!!!!)lbs and 28 months.
I noticed you said you cut out red meat. I think it is totally fine, whatever you like. But if you still want to eat beef sometimes, consider grass fed maybe. It is full of healthy omegas and is actually a very digestable meat for humans. We need protein to grow and lose, and chicken can get boring. I don`t know what is avaiable near you, but we live in the country, so I have been able to find grass fed beef and free range chicken and pork for us, and it tastes great and I feel so much better about eating and feeding meat to my family.