It will likely be hard to find much of any information on the medal and the association where the Shoot occurred. Roughly translated, the medal was awarded by the Central German Protection Association in Escherheim and is likely where the Competition Shoot occurred. Also, since this occurred before WWI and WWII during the German Empire or King's Empire, there may not be a lot of info around except in some German books that survived WWII. You might contact some officials in Escherheim (a city district of Frankfurt am Main) to see if they can provide some information. My ex-wife had an Uncle, Aunt and Cousins who lived there, who we visited one time while I was stationed in West Germany.
I scond that.
Only thing Ifind a bit odd is that the "Middle German" (=today eastern Germany) had their price shooting in Frankfurt.
I understand but without some context (documentation) or clarification from someone who knows, we really don't know whether the "Middle German" referred to a region (this could have encompassed a very large region in Germany before the split and especially during the German Empire) or if referred to a classification of people (i.e. for a time and some may still do, classify certain people in Germany by their' job, job title, status and where they lived). This old thinking seemed to be left over from the feudal times.
As a native speaker, I never heard "Mitteldeutsch" other than regional. The "middle class" is somewhat of a post war phenomenon or invention. Pre-war they would have called themself "Bürgerlich" (Citizens, Citoyens in constrast to farmers or proletarians). What makes me however think twice is your notion that the region was pre-war defined larger (now: East Germany south of ex-prussia) and that wiki lists Hessian Dialct as "Mitteldeutsch". So, from that definition Frankfurt would fit in...
Greets Namxat