I came up with a solution, not sure if it’s a great one but seems to work:
In header.php, add a div with relative positioning (I put it in just after the header img code):
<img src=”<?php header_image(); ?>” width=”<?php echo $header_image_width; ?>” height=”<?php echo $header_image_height; ?>” alt=”” />
<!– ADD TEXT TO HEADER –>
<div style=”position:relative;top:-65px;left:620px;width:400px;height:60px;”>
Text to be added
</div>