Solved it, after a long struggle, and then a single search on google. It was the second link returned and the only one I clicked on!
So based on the example I found i added
background-size: 766px auto !important;
to the media query for max-width: 359px where iphone size kicks in and it works (it's setting the width on my background image until it's height matches the space available.
I missed this because it is not set in the css file for the theme, but in a js file - custom-header.php, in the inc folder.
Repeat every day ten times: google is your friend.