I'm glad to hear that I helped! As I said, I haven't found any Fringer's in my lines yet, just trying to help out while I could.
You might want to pull the 1910 Cleveland Census data for Edward C Fringer's family too since he's also born in Switzerland and of the right age (56) to possibly be a brother of your Harry. (Or a cousin perhaps.) Edward has a brother, Benjamin (age 46), living with him. The family is located in the city of Cleveland, enumeration district 0260, Visit #0074. If he's part of the family, it might provide another avenue for tracing Harry Sr.'s parents. Edward has a wife, Mary (43, b.PENN), and children: Harry (16, b.OH), William (13), Lawrence (11), and Leona (8).
There is also a listing for a John Fringer in the 1910 Cleveland Census. He is 62 and born in GER. Wife Anna, 60, born GER. Located in the city of Cleveland, Enumeration district 0249, Visit#0433.