If it's your goal to remove the haze or glow around the Moon, you could try adjusting curves in PS, may need to create a mask. The distortion is a whole other matter. Very low altitude Lunar shots are most often eaten up by the dense atmosphere. The distortion is near impossible to correct, especially if taken at high focal length. Unfortunately stacking won't remedy what you've described, although there's certainly no harm in trying. Post a shot so we can see what you're starting with.
I spent all night last Saturday(night fall to dawn) shooting deep sky and come to find out that I was a hair out of focus on all my exposures. I knew it would be less than I wanted but I went ahead and stacked some anyway. Not the results I was after - poor data in, poor data out. A night wasted but not completely, it was still fun and I learned a lesson, again.