I've never seen such a problem with movement in the moon - it's normally slow enough that you don't see it.
As you've discovered the problem with DRI is that it increases the amount of noise in any shot as every "new" exposure you make is from the same original file so the noise is in exactly the same place so you enhance the noise along with the image.
As for impact, the scene doesn't really have any obvious direction to it. I think this would work better in a panoramic crop which puts the moon closer to the top of the frame. Your eye is drawn up the frame to the moon and then it keeps going into the empt sky and if you removed that it might help.
I like the panoramic crop a lot more. It's a shame the moon is in the middle of the frame (horizontally speaking) as it would be better placed in a rule of thirds style but this is, in my opinion, much better.
I must admit that I'm still puzzled by the amount of movement you got in the moon. How far apart are the shot times in the EXIF data?