I thought I would share my resolution with you here.
I tried a variety of things, including lengthy web.config changes per recommendations on Unity's site, and others found in other forums, but the only thing I ended up needing to add was the following code to my Startup.cs file in the Configure() method:
StaticFileOptions option = new StaticFileOptions();
FileExtensionContentTypeProvider contentTypeProvider = (FileExtensionContentTypeProvider)option.ContentTypeProvider ??
option.ContentTypeProvider = contentTypeProvider;
The main point being that files with the extension ".unityweb" were located in my \Build folder and were the ones being used, despite the option being selected to use Gzip compression. Once built I never ended up with any *.unity3dgz file extensions.
However, if your release does contain files with those extensions, you might want to try adding another Mapping for that, for example: