These sentences are correct and natural. You could just use past simple, however, as present perfect is a present tense, so we know the past simple action happened before. I've never even met my uncle in person before. He moved to Italy long before I was even born. I've never even met my uncle in person before. He moved to Italy a year before I was even born. It's more important to use past perfect with another past tense to indicate that that action had happened first. I'd never even met my uncle in person before. He'd moved to Italy long before I was even born. I never met my uncle in person. He'd moved to Italy long before I was even born.

The repetition and tense aren’t too natural. I’ve never even met my uncle in person. He moved to Italy long before I was born. (Of course it only makes sense in a context where living in Italy would make meeting him impossible.)

"Before" serves no purpose. "I've never met my uncle in person. He moved to Italy long before I was born" "He had moved a year before" adds nothing of importance to "he moved a year before"

Both sentences sound natural. The first sentence is more general and simply states that the speaker has never met their uncle in person. The second sentence provides a bit more detail by specifying that the uncle moved to Italy a year before the speaker was born. Both sentences are grammatically correct and convey the intended meaning.