I spoke to my elderly mother and she said she thinks that your Fiala family is connected to our Fiala family. Mama thinks it that your Fiala's are descended from one of her father's uncles or maybe from one of her father's brothers who were unaccounted for after WWII. There were 4 brothers and only my grosspapa and one of his brother's were accounted for after the war.
I know my grosspapa was born in 1900 and his 3 brothes were younger. I will ask mama to translate the Austrian birth certificates for me and maybe I will have more info.
Mama said her grosspapa's name was Theodor Fiala and he had several brothers including one named Joseph Fiala who emmigrated to America either in the late 1890's or early 1900's. Teodor was a tax collector for Vienna.
If your uncles in Austria think any of this info fits, please email me back at email@example.com