In a comment to my original question, @SJP gave a link to @Frank Bakker's answer to the question at Calling Roslyn from VSIX Command. This does work as outlined.
@JoshVarty provided a hint of the direction to go in his answer above. I combined that with code provided by @user1912383 for how to get an IWpfTextView answering the question Find an IVsTextView or IWpfTextView for a given ProjectItem, in 2010 RC extension. Here is the code I came up with:
var componentModel = (IComponentModel)Package.GetGlobalService(typeof(SComponentModel));
var textManager = (IVsTextManager)Package.GetGlobalService(typeof(SVsTextManager));
IVsTextView activeView = null;
ErrorHandler.ThrowOnFailure(textManager.GetActiveView(1, null, out activeView));
var editorAdapter = componentModel.GetService<IVsEditorAdaptersFactoryService>();
var textView = editorAdapter.GetWpfTextView(activeView);
var document = (textView.TextBuffer.ContentType.TypeName.Equals("CSharp"))
? textView : null;
In a comment after @user1912383's code mentioned above, @kman mentioned that this does not work for document types such as .sql files. It does, however, work for .cs files which is what I will be using it with.