Here was the solution that worked: iterate through all entries on the page, look for a image, attach the classes to the H1 and first p tag. Prepend the p containing the image above the H1, as the first child of the entry div.
<div class="entry">
<h1>Headline 1</h1>
<p><img />Image? Yes</p>
<p>Some Text that needs to stay put</p>
<p>More copy text</p>
</div>
<div class="entry">
<h1>Headline 2</h1>
<p>Text in a non image entry</p>
<p>This text has no image to keep it company</p>
</div>
$('div.entry').each(function(){
var $this = $(this);
if($this.find('img').length > 0) {
$this.find('h1').addClass('home-h1-adjust');
var $img = $this.find('p').first().addClass('home-p-img-adjust');
$this.prepend($img);
}
});