iTunes days "Software for this iPhone is not currently available. Make sure you have the latest version of iTunes and try again"

I have a one day old iPhone 6 with a screen that's gone black. It doesnt' appear to be dead because if I plug it in, iTunes can see it.

It says it's in Recovery Mode, and offers the option to restore it. If I click that, it says "Software for this iPhone is not currently available. Make sure you have the latest version of iTunes and try again". I've got the latest iTunes.

Is there anything I can do other than take it to an Apple Store?