This must be extremely frustrating. BA do sometimes (!!) make errors and are known to be slow at fixing them. They might tell terminological inexactitudes in their replies, even tell lies, but they do not normally set out to defraud people.
However, to get it resolved, you need to take rather a lot of relaxation exercises. The words and phrases you are using on here will not lead to a resolution. That is just the way the world is. Relax first!

First of all, in which country was your CC issued? What are the laws about disputing charges? In the UK it is, as others have said, a relatively simple process, especially if the CC issuer thinks you are a good customer. I have disputed charges in the past and it has been quite simple. (It isn't always).

Next, find a way to contact BA that gives you confidence that they will respond sensibly. As others have said, once you have Formally notified them of your case, they will eventually respond. They are not quick.

14 calls to a non-empowered contact centre will not do it.