OK. So the problem with the mnemonics in the custom command was due to an error in my code. I was explicitly settings the Header attribute as well as binding to our custom Command class. Since the explicitly set attribute trumps the command's text property, we didn't get the benefit of the mnemonic under the 'x'. So, if you change the the contents of Properties.Resources.ExitText to "E_xit" the application will respond to Alt+F,x just like we want it to.
Now, I'm not sure how to add a mnemonic after the fact to the built-in ApplicationCommands.X objects. I can understand a reluctance on the part of the framework developers. They have no way to determine which commands will be in the same menu, so they have no way to guarantee that each menu item has a unique mnemonic. I just wish I could find the a way to set the keyboard shortcut for the built-in commands without explicitly setting the text. That would sort of kill the automatic localization aspect of the built-in commands.