Sorry! We don't currently support Integrated Windows Authentication for Deployment Manager.
This is something that we're currently looking into, and I've asked our Program Manager to get in touch with you to talk about what your needs are in this area.
If you go back into IIS Manager and turn Windows Authentication off, and turn Anonymous Authentication back on (don't worry, Deployment Manager has built-in auth on top of what IIS provides), then the SSMS add-in should start working.
I suspect that it was the permissions change you made that meant the Deployment Manager UI started working, so hopefully this auth change won't break that!