Oh how wonderful to hear from you!. I thought Pereszteg might be the place I was looking for but never for sure till you hear it from another source.
The Rokops that are in the family are the only ones that I know of and they all came to America. I never found any females coming over:
Janos born 1869 -- Don't know what happen to him. On the ships list it states he was married but other then the ships list that is all I have of him.
Jozef born January 4, 1879 He is the one who came over first and everyone went to his house when they first came over - everyone mentions his name on the ships list.
Geza (Victor) born April 8, 1880 came over with his wife Antoinette born 1880. With their 2 children Victor born 1902 and Isebella (Zelda) born 1905.
Gyula (Julius) born April 8, 1884.
Are any of these in you line of the family?
Other names that I have here and there are Grasli, and Folyi. They all came from the same areas and married when they got over here.