That's a good idea! I hear you on avoiding medicating! I will say, I feel like Betta fins take FOREVER to heal...so, you may be doing everything right, but progress might be slow...as long as you're not going backwards, you're going forwards!
50% change once a week is pretty solid...how big is your community tank?
If you don't see a positive change when you remove the tetra, you could also try separating the Betta.