I've definitely faced the same issue of wanting to use an ethnic name but not having origins within that place, so I understand your dilemma and am curious to see what others think. If you're uncertain about using an Italian name, then I would suggest straying away from Gianna (<- though I like this one too!), Giovanna, Giovanni, and Giuliana (unless you used the more "American-ized" spelling Juliana) since all of these sound very Italian... I have a hard time picturing a Giovanni Miller or Gianna Roberts!
I think that a lot of the names you mentioned, however, are very usable because they've become more commonplace in other cultures. Luke and Lucy are popular, so the variants Luca, Lucian, and Lucia don't seem too far off. I think Sebastian is incredibly usable as well; I've met several Sebastians of various ethnic backgrounds. As for Leonardo, I think Leo is more usable on its own... Plus the namesakes Leonardo da Vinci and Leonardo DiCaprio (both of whom have very Italian-sounding last names) may be hard to shrug.
I personally really like Gemma and Tessa, both of which are Italian
Hope this helps!