It sounds to me that the paintwork is oxidised and therefor the surface of the paint will have texture that is full of craters if you could look at it under a microscope. You need to have it wet flatted down to remove the oxidised surface, then machine polished. After that use a UV resistant sealer/wax to preserve the shine. You would only need to flat the faded surfaces, so colour matching will not be an issue and originality will be preserved. May be worth getting a paint thickness test done to if it’s been polished before(especially on body line edges)
Hope this helps - you could always try one panel or part panel as a test.