Okay...this post spurred me to check something I've been wondering for awhile.
I just aimed my camera (K-30) at one of our under-cabinet fluorescent light bulbs, with a good bit of the cabinet in the frame. As expected, the bulb was pretty washed out in liveview. The bulb has a brand label printed directly on the bulb at one end, and this label was not discernible in liveview.
However, I tried switching the auto exposure setting to center/spot, and lo and behold, I was suddenly able to make out the printing on the label! The exposure in liveview was able to adjust to make this possible. Aiming a little off of the label (to force the center AE onto the cabinet), the label blew out again.
So, to the OP, there may be hope yet! Try switching your AE setting to center/spot, and put the moon in your crosshairs. I can't see the moon yet here, so I can't test for you.