I spent enough time on this, and I couldn't find answers here, so I hope this helps someone:

Our setup is DNN 5.3.1 running on IIS7.  We are running 2 IIS Servers in a load-balance configuration.  The DNN application files are on a network share server.

1. Create an Active Directory service account for your web applications to run.
2. Turn on impersonation in web.config to use that AD account
3. Make sure that the AD account has full control over the location of your application files on the network share
4. In the "Basic Settings" of your DNN application on IIS (virtual directory), set the "Connect As..." option to that domain account
5. In IIS Under "Application Pools", select the "Classic .NET App Pool" (which DNN requires you to use) and right-click, choose "Advanced Settings"
6. In the "Process Model" section under "Identity" enter the credentials for the AD account

I hope I didn't leave anything out.  I haven't been documenting my steps along the way, and it's many work hours of trial and error to get to what is essentially a simple solution.

Thanks Eric!

PS I'll move this to the Installation forum ...