Way to go the extra mile, Reclaim.
The issue with directory confusion is because if you run Site Publisher with a few different templates, it can create several different asset directories. So as Jim (that is you, right Jim?) mentions, any customization calls for dissection of the source HTML/CSS.
At te point you are trying to finagle this is when you can realize that unless you are okay with the simple results of Site Publisher, you can move away and consider working directly with the HTML5up theme this is based on, or maybe try a Wordpress site at the main URL with a landing page theme.
I have done customization of this theme for a friend, and you need to do more than a square image to get a nice effect; While this image is pretty, it will not work well because the cropping cuts off the sites. You need an isolated item, on a background colored #348cb2 and the image should be the same dimensions as the original (1500x500 to work the same). Here is one I did for a friend’s site that is a farmers market:
I tried doing some photoshop erasing on Peg’s image, but it look pretty crappy:
Frankly I think her site calls for puppies
Upload any of those to
bg.jpg and you might get something like: