Thank you for bringing this up again.
Consider it officially fixed.
This is one of the most enigmatic issues I've run across since I started this over 5 years ago.
The ultimate cause was the gallery preview section, oddly enough.
Here's a basic breakdown for you, if you're curious.
Initially, I suspected that the load balancer was double-issuing requests, which was something that has happened in the past when for whatever reason the load balancer thought one of the servers was down and reissued the request to another server.
But the fact that it wasn't happening for me on the DKPSystem main page or my guild site more or less indicated to me that that wasn't the case. So I delved deeper and found that every page on your site was actually double-issuing requests, and that they were being issued by the browser.
The log files on the server would first indicate the original REFERER header, and then there would be a duplicate request with the target page as the REFERER header. This could be caused by some kind of javascript redirect.
So commenced several hours of reading over the HTML and javascript of your site (both the generated template code from your custom layout and the raw layout.html file you use) looking for something, *anything* that would look like a separate request. A javascript AJAX request, a redirect, or a meta tag redirect would be the obvious culprits, none of which existed. I even had a moment of panic when I saw that the page was loading a pastebin.js file, which I thought your site had been hacked (as pastebin is a common dumping ground for keyloggers), until I realized it was one of my chrome plugins (lol, so dump).
I disabled javascript and found that the problem was still happening, which really got me wondering. It happened in both Chrome and Firefox (I run Linux so I couldn't test IE without walking into the next room, but it was unnecessary).
I fired up Wireshark to sniff the packets, and found the duplicate requests there as well. I was hoping Wireshark would give me some insight, but to no avail.
I tried using wget to download the pages, thinking that it would also duplicate requests in the log, but they weren't. Wget was issuing a single request. So something about the browser was issuing the double-request, and it wasn't javascript, since javascript was disabled, and it wasn't a meta tag redirect thing.
After searching a bit on google (which turned out to be a difficult search query to write), I came across someone mentioning that an <img> tag with an empty "src" attribute would load the current page as the src (something of which I was admittedly unaware), and I looked over your page's code to find exactly that, but it was in the gallery preview.
The page made a dummy, supposedly empty <img src=''> tag which would then be loaded with the cycling images when the page loaded. I replaced it with <img src='about:blank'> so that it's just an empty request to the browser default and viola, problem solved!
And since I don't use the gallery preview on my guild site or on the DKPSystem.com site, I wouldn't have noticed it.
So there you have it!
I've tested the fix and pushed it out to the production servers already. Thanks again for keeping on me to fix this elusive bug.
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It's all in the reflexes.
