I'm sorry that I can't answer your question, and in fact have a question for you. My paternal grandfather, along with his siblings, immigrated from St. Ivan, Hungary around the same time as did your grandparents. Actually, they also settled in Ohio—Cleveland.
I'm planning a trip to Budapest but want to see if I can find where my grandfather came from. St. Ivan is not on contemporary Hungary's map. Do you know anything about it? If it was called something else is Austria-Hungary?
Many thanks. Good luck finding out more about your grandparents.