When I saw my first specimens of today's brachiopod I thought it was a Xystostrophia. I was close as the form is similar but, in North America, it is more commonly referred to as Eoschuchertella and what I'd found was E. woolworthana. The species is cospecific with Xystrophia woolworthana and has also been assigned to other generic names like Schuchertella, Orthothetes and Strophomena.
Eoschuchertella woolworthana is semi-elliptical with a wide hinge line that is roughly equal to the width of the shell. Inflated specimens have a very convex brachial valve with a flat to slightly convex pedicle valve. Along the hinge line there is a very wide, obtusely triangular shaped deltidium on the pedicle valve that extends away from the hinge. The surface of the shell is covered in fine radiating striae.
Specimen #1 - Brachial valve
Specimen #2 - This one is flattened but you can still see some of the diagnostic features.
Here are all three of the specimens side by side for size comparison.
Eoschuchertella woolworthana looks very similar to Xystostrophia umbraculum as you can see with specimens of the latter from Poland and Morocco.
The Kalkberg formation is lower Devonian in age (Lockhovian to Pragian
stage). I collected these specimens from a roadcut near Shoharie, NY.