Even with morning effect the moon is still brighter. If it wasn't brighter than the surrounding sky it would be invisible (like the shadow side of the moon). But I understand you only had 2 colors to work with. You could do something like this, maybe, but I like the color balance in your version better. 

I tried to replicate the morning moon effect, where the sky is bright but there is still a visible moon, happens a lot here where I live!
example (not my picture)
 

Very nice use of two colors. Great readability, although I don't know how I feel about a dark crescent moon.