I since learned this applications is based on .NET Framework 4.8 with WinForms.
Wine
Installing .Net Framework from Making sure you're not a bot! I still got an error:
Unhandled Exception:
System.NotImplementedException: The method or operation is not implemented.
at System.Drawing.Font.FromLogFont (System.Object lf, System.IntPtr hdc) [0x0009e] in <993b785229084ceebbb252213aea31a1>:0
Removing .NET Framework again (with wine uninstaller --list, wine uninstaller --remove "{...}") and installing dotnet40 with via winetricks seems to have gotten me a working application!
Now how to wrap this in a derivation - will read What is your approach to packaging Wine applications with Nix derivations? 
mono
Running Windows Forms on Linux with Mono and WinForms | Mono do give some cause for optimism that this could work after all