Thanks for the comments everyone. James, you raise many interesting discussion points. Yes, it is purely luck to get the right conditions. I've started keeping my Nikon with 70-200mm lens ready to go at all times, so that if I see something materialize out the window I'm ready to go outside. I looked back at my image files, and I was only capturing images for a ten minute period, during which I took 26 images. I was very selective in the images that I took, because most of the time the Moon was either too free of clouds, or completely blocked by them. As you say, the cloud cover has to be just the right amount to bring the exposure of the Moon down to the level that simultaneously exposes the clouds. Even then, most images produced are fairly uninteresting. Out of my 26 images, two were interesting. The one I posted above was my first choice to process because I liked the interesting ring of blue clouds that surrounded the Moon. I have spent a good deal of time processing that image and have created multiple versions. It is hard to decide which to post, because my feelings towards each version changes depending upon the lighting conditions in the room (day or night). This is related to the point that came up in one of your recent threads, where I said that films are edited differently depending on the expected audience viewing environment.
The other image that was worth processing is posted below. This one used a 1/8s exposure. My method here was to keep aperture constant at f/2.8 and then adjust the shutter manually according to what produced an image of the Moon that was as far exposed as possible without saturating. It's worth noting that a 1/8s exposure of the Full Moon is highly unusual, and indicative of heavy obscuration. A typical exposure at f/2.8s of the full moon would be 1/1000s, which is 7 stops (128x) greater than 1/8s.
If we look at the raw file without any editing, we see the image below.
Although dark, we can easily see some clouds, which is a good sign that the exposure was optimal. In ordinary circumstances, a proper exposure of the Full Moon at night will render any foreground elements completely black. But here the clouds have reduced the brightness of the Moon. If we analyze the histogram of the Moon itself, we see that the exposure was essentially perfect for these conditions, with the average intensity of the Moon at a tonal value of 117, which is middle gray, and no pixels are saturated. This means we can adjust the exposure up by 2-3EV easily in processing, and then bring the highlights back down to achieve a result that balances Moon and clouds. And this doesn't require any manual selections or layer masks, but simply global edits in Photoshop.