I have just started working on this line.Do you have any info on the Alberti's from before they came to America?It sounds like they were a well known family, and I can't help but think there would be records of their life in Italy.
How are you connected?
I am descended from Josse Gosselin and Elizabeth Alberti / Albertus' son Samuel, through his son William, his son William, and his son Marvin.
Since you mention Leverich, I think there must be more ties, as Samuel Gorsline married Martha Leverich, descendant of the Rev. William Leverich.
I will be happy to share what I have with you, though it's not much, as I just started working on the Gorsline line this far back.