Moon tilt against the horizon in a single day
Mooncalc.org offers a pretty comprehensive set of tools for viewing the moon.  Click on the location you want, then drag the slider on top through the day to see which direction's sky the moon will be in (or times where it will not be visible).  And it shows the moon's shape you will see (I presume that's as viewed with nearest horizon down?)
(For those interested, suncalc.org is their sister site for the sun.)

I'm not an astronomer, but this article from Goddard Space Flight Center looks like it offers a very solid discussion of libration, and the causes due to moon's orbit, the relative location of the moon from different viewing locations, and the tilt of the Earth in relation to the sun.