The reason they are not responding or not answering the phone is not due to the current fire. My day hike permit was for June 14 and I emailed the Eastern Sierra Interagency two weeks before and never got a response (emailed three times). I called every day - no one picked up. So, I drove to the Visitor Center the day before and waited in line for my permit. There was no one behind the desk issuing permits when I arrived. I waited over an hour and finally someone showed up. The employee was very nice and told me that they are severely understaffed.
You're going to have to go to the Visitor Center and get your permit. Get there when it opens. Be prepared to wait. However, with this developing Inyo Creek Fire in the area, you'll need to monitor and check if the road is going to be open to the Portal.
Let's hope that fire crews get the upper hand on this fire quickly!