I guess it wasn't a totally wasted evening as it was a good learning experience. I got some advice from friends and found a couple of good articles on photo.net which helped. But I was too slow changing settings before the moon moved out of position, which made trying to do a composite shot in Photoshop Elements very tricky, especially since I have barely any skills at all in that program. I should have used the self-timer again, and bracketed the exposure, to get a better selection of usable shots. Among other things.
I can't believe I actually spent the whole evening on this one crappy photo...