Hi Josh,
It could be possible with some JS.
You can add this under Custom > JavaScript in the Customizer.
jQuery(document).ready(function($) {
var html = '<img class="my-header-image" src="http://www.thejewelrycenter.us/images/hdtxt-01.gif">';
$( html ).appendTo('.x-navbar-inner .x-container');
});
Let’s change the image path with your uploaded image on the new site.
And then add this under Custom > CSS in the Customizer to position it better :
.my-header-image {
float: right;
margin-right: 20px;
margin-top: 10px;
}
Cheers!