See https://goo.gl/cTu7af. How close can I come to designing a header like this in your theme? I think the top header would have to be taller in the theme and everything else should work within it.
You can do this with the Top Header Row. Active the Top Header Row and change the height of it. Add a Widget Element (Media Widget) and a text element.
Let me know if you have difficulty to achieve this.
