It's true that the eye response is logarithmic to overall brightness, but that does not mean that you see something faint next to something bright nearly as easily if you make the bright thing ten times brighter.<p>The number of stars you can see at full moon is already very limited now. I'd guess that the limiting magnitude goes from 6 to 3.<p>I'm not sure it would have made a big difference for latitude determination. It's already readily available by measuring the noon height of the sun.<p>About using the moon, have you read the book "Longitude"? It's a really interesting book about the quest to measure longitude. To measure it, you essentially need a clock that is independent of local time. I doubt the rings would help there. While <i>in principle</i> you could use the phases of the moon, you need the time to an accuracy of at least tens of minutes to be useful, and that seems very difficult to accomplish with the Moon.