Did you ever think that there could be a faint cloud deck since you're not that close the moon set ?
No clue. There's just too much difference between the dark bay and the bright moon. Besides, I think the photo looks good just the way it is.
I do like the idea of taking two shots. One of a well exposed moon and the other of a well exposed bay. Then overlay them. It's probably the easiest solution. HDR might work but there's a lot of difference in exposure between a moon that's as bright as noon time sun and a bay that's lit only by a few electric lights and the moon's reflections.
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