Couldn't you take the moonlight and "compress" it, say with a cinder block, thereby making it into a more concentrated form? You would get the same wattage per mason jar, if it was under pressure.
I use a box full of angled mirrors to capture light - the light enters in through an opening and starts bouncing around on the mirrors, confusing it. Once the box is full, I close the lid, trapping the light inside. At the bottom I have a spigot that I use to drain the now tamed light into a mason jar , and once I close the lid, I have a lantern that lasts most of the night, until the light dies.
Here is a tip - Adding a little bit of water and fresh cut flower food to the bottom of the mason jar feeds the light, and often you can get it to last until daybreak. Then its just a matter of dumping the water, flower food, and dead light into the compost heap for recycling, and then you can reuse the mason jar later that night.