the Feuersteins came from Schwarzenberg, which is a village in the region called Bregenzerwald (Vorarlberg). As far as I know he (or they) left around 1700 for Elsass. Your theory concerning the reason for leaving seems quite accurate. Many men from the Bregenzerwald migrated annually during the summer to Southern Germany, Switzerland and Western France to work as masons, plasterers or carpenters. They followed the famous masterbuilders (Barockbaumeister) who prefered workers from their own country. Quite a few of those masons married there and stayed for ever.
It will be pretty hard to find your Feuersteins in the parish records, because there where many Feuerstein families in Schwarzenberg and the records for that time are imcomplete and in the most cases they have no notice showing a possible emigration.
Cornelia Albertani from the States Archiv in Bregenz can tell you, whether there is a chance to find your family or not. Her e-mail: firstname.lastname@example.org
I guess you know the booklett "The Origin of the Family Fireston" which was published in Akron/OH (no year).
So far for the moment
Meinrad Pichler, Bregenz