Here's how I do it:
On your "Moon aligned" image, change the selection type from square to circle, and set a feather of 2 pixels.
Select an area a few pixels larger than the moon, and ctrl-C (copy).
Then just paste that selection over your "feature-aligned" image. It will be pasted as a new layer.
Then just use the move tool to move it in place over the moon. I just use the arrow keys, and use the "eye icon" to "blink" the layer on and off to be sure you've aligned the "aligned-moon selection" correctly over the old-moon.
It's the feather that will ensure you don't get hard lines or edges when it's pasted over the top.
Let me know if you get stuck and i'll post some screenshots.
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