i misunderstood what you said you did, or want to do ..
i thought you were making solar graphs, and for some reason
you just "opened up" your pinhole camera to expose the paper to the moon ? ...
as you could tell from my initial response, it didn't make much sense to me ...
i didn't realize you wanted to do the same thing you were doing with the sun, but ... with the moon ...
you might consider doing a "dry run" with an actual camera with a lens to make a shorter than 3month exposure of the moon.
i use box cameras when i do this sort of photography, i don't usually expose the paper for longer than a few hours ( a half - day was my maximum )
and i usually do it during the daytime, so i have full uv + blue light to work with.
i attached one of the last ones i did, its 3 sheets of 5x7 paper taped together
in a home made 15x5 box camera.
i don't think you will have much trouble though, if you plan where you put your camera
and use a really wide pinhole-aperture to make sure you get the rise of the moon when it is different ...
seeing rise and set position of the moon changes depending on its phases and the season
these might help you determine where you could set up your camera / pinhole camera
one gives an idea of where in the sky the moon rises + sets, the other is a planetarium sky-chart .
good luck !