This is what the moon lights are (-Three 1 watt Lunar Blue-Moon-Glow 470nm LED lamps.)

Are you running the "moon lights" just a few nights per month, like the real moon? If you do that I don't seee why they couldn't be on all night long. Last night was the first night with them on. At the present time I have the time set to have them on all night and every night.

If they are too bright they will inhibit some nocturnal inverts from coming out at night, you may want to compare the amount of life you see. Check at the same time each night when you use the moons lights vs. when you don't, that will give you the answer you are looking for. In my tank I have noticed that certain inverts will not come out until the tank is completely dark, actinics and all. I did notice that my cleaner shrimp and perpermint shimp didn't come out. The blue leg hermit crabs did seem to come out same. The star polyps, where the moon light was hitting, didn't close up fully for a couple of hours.
This morning the star polyps were open again where the moon light was hitting.

Thanks Alan and Danny for your coments