@dumpling I think I'd like to try there's only two potential pieces of info that I don't currently know that could hold me back.

Whether my great-grandparents emigrated after June 14, 1912 (I believe my great-grandfather served in the Italian army in WWI, so I think I'm good there), and whether they retained their Italian citizenship when my grandfather was born (which given the rampant bigotry and lynching of Italians back then I wouldn't be surprised if they chose to give it up)