Since you are in the US this might help, as you still have a few hours before dark. I came home an hour ago 18:00 GMT and the sun was not yet quite set, but the moon was well up over the horizon and showing quite well. This is a good time to shoot the moon, while having plenty of detail in the sky/background. Also to get a good shot of the moon with detail you need a long focal length 300mm is probably as short as you want to go, although 400mm or even 600mm would be much better. To then get some scenery etc in the background you need to be a goodly distance away from it while still keeping the moon looking large in the frame. If you don't use a really long lens even if you have the exposure correct you still wind up with a tiny little dot for the moon.
To be frank although the full moon looks great with the naked eye, it is actually very flat as the sun is falling directly on the surface. The moon looks much better when shot at about half way, as then the moon is more side lit, and there is more definition from the shadows thrown by the surface features.
Here's an example of what I am talking about, a few years ago I was shooting an airshow at the IWM Duxford, and there was a nice bright crescent moon right in the middle of the day, and this was towards the end of May by the way. So anyway I took some shots of the moon at 400mm with a 100-400 L (original version obviously) as that was the focal length I was shooting with mostly on the zoom. Unfortunately thanks to the positioning of the flight line it was not possible to get the aircraft and the moon nicely aligned in camera. By using the same FL for both the aircraft and the moon it was very easy to combine both images in PS, with no problems caused by resampling either image. This is the final image, the two frames were merged at the original size, but the image was then extensively cropped too, to get the frame to be filled.
IMAGE LINK: https://flic.kr/p/eaXKD5
Hey-Diddle-Diddle!
by
Alan Evans
, on Flickr
This is an out of camera shot,at almost the same FL, 390mm against 400mm for the composite, and is also uncropped, just to show how close together the aircraft and the moon actually got. Sometimes you just have to help things along a bit
IMAGE LINK: https://flic.kr/p/eaS93X
Sbach 300
by
Alan Evans
, on Flickr
Hope this helps and offers some useful ideas.
Alan