Hi Kirsten, I'm back again and still researching. I did find some interesting information. You had mentioned a James Sposta thinking he was one of the children of Andrea Sposta and Catherine Colangelo. However, I did find James Sposta in the Port Chester, NY census -- his parents were Anthony Sposta and Mammie. He was the only child mentioned in that particular record -- will have to look it up again to give you the year.
I searched in both the San Martino and the Avigliano records for Sposta/Esposito but found nothing.

However, Andy DiBernardo, brother of Rachel, Virginia, etc.
told me that the family would visit an Esposito family in Port Chester several times a year. I am in the process of following up on that lead. So far no town of origin.
But I did find a SS record for Angelo Esposito b. 1887 - he was also naturalized so I am trying to see if I can get his naturalization papers to find the town of origin. Will keep you posted. Susan