OK - lemme clear something up about the Amish.
The Amish in general, which includes Mennonites and Old Order, have been adapting modern livestock methods in order to make money. Lots of Amish families, not a lot of land to farm. So they either go to work in the factories (RV factories for the Nappanee/Goshen/Shipshewanna, IN area) or they utilize the 10-12 acres they managed to find and raise poultry or some kind of livestock on a couple of acres of it.
As far as raising birds go, they have large poultry sheds for cramming in as many as possible. There's a brand of duck breast that Costco carries. I knew one of the families who supply the ducks for that company. If you didn't ask, you'd never know there was anything in the building it was that clean. Larger animals such as swine and cows either come from small time producers or large co-ops.
Kenji - you may not get a straight answer. Chances are the people at Calma have developed relationships with different families and don't source everything from a couple of farms.
I spent a lot of time going back and forth to what we called Amishland for many years. I got to know them and their lifestyle very well. I'm more than happy to answer questions about them and their farming methods.