Just because a few well qualified doctors told you it's eczema doesn't mean EC is eczema. Many other people, including myself, have seen many very qualified doctors and many of them all say different things. For instance I have seen two very highly qualified Psoriasis and inflammatory skin disease specialists (both of which I'm positive are as qualified as your doctors) and both of them strongly believe this is Psoriasis. But that does not mean it is.
And as far as being diagnosed with EC that is contradictory to what you have said. Your were diagnosed with eczema. Exfoliative Cheilitis is just a description of our symptoms, and this name has nothing to with the cause. Which means that, just because one person who has Exfoliative Cheilitis (AKA Inflammation with peeling skin), was diagnosed with Eczema doesn't mean that Eczema is causing everyone else's EC. This is what people have a hard time understanding.
And those symptoms you listed are all very common in so many skin conditions, so those symptoms alone definitely don't diagnose this as eczema.
Anyways I respect your opinion that this is eczema, as it is definitely a possibility. But your evidence to back it up just isn't conclusive enough to say that "EC is eczema".