Sorry, but I have only literature about the Harrachs in German.
But I could give you some informations about the Harrachs.
1. No Harrach ever beared the first name "Peter" - and they beared a lot of first names. As we say: as a Harrach you are not called Peter.
2. I wonder, whom your cousin met, because the last count of Harrach lives in Bruck a. d. Leitha, not in Rohrau. In Rohrau lives only his grand-cousin Countess Waldburg zu Zeil née Countess Harrach.
3. There was a famous painter named Ferdinand Count Harrach, who lived in Breslau in the 1850ies. There he went to school and spent his military service as Kuerassier.(Kuerassier = special kind of cavalery). Maybe he had a girl friend there....
In 1869 he married Helene Countess Pourtalès and had six children with her - but no Peter.
The father of Friedrich was Carl Philip, born in 1795, who also lived in Breslau. He also had no son named Peter or Georg. But maybe he had a girl friend...
If one of this lineage would have had children with a girl friend, this children would not have been members of the family and they never were counts. Maybe they got the last name Harrach - I wonder how - but in 99 percent of this cases you will never find a church record with the real fathers name. You would need a specialist to get a (near) proof.
What you need are european church records. Maybe your great grandfather changed his name with his arriving in the USA. Maybe because his mother told him this story or something else.
4. That your great grandfather came with the coat of arms or a family tree on a scroll has absolutely nothing to say. a) You never saw this coat of arms or this family tree b) Why did your great grandfather leave europe when he was a count?
5. I am member of the "Adler", which adress you have. And I am specialiced in the genealogy of the austrian nobility.
Please keep in mind, that genealogy is a step by step-research. You will need every date of birth, marriage and death in your family, that you could get. You will need the name of the ship, date of immigration etc. etc. before you will get more informations about your ancestors. But please forget the idea, that you are a member of the Count-of-Harrach-family. The members are well known - since 300 years.