Unfortunately, because (I'm assuming) the lack of foreground/background contrast, the software threw down align-points all over the place, and I wasn't having much luck setting them manually. So rather than continue to play around in Registax, I fired up Photoshop to see what I could do with my hazy images. Between using setting a duplicate layer to multiply, opacity settings, and brightness/contrast adjustments, I was satisfied enough to share.
Below is the image the above is processed from. For what it's worth, it's 1/30th @ ISO100.