However, would not a 32-mile wide disc, 15 miles up in the sky, occupy about a quarter of the sky? If I recall correctly, both the sun and the moon occupy less than a 5 degree arc of the visual field.
Please hold while we compute....
We care about 2t, the angle the moon occuppies in the sky. Making a right triangle from {me, center-of-moon, edge-of-moon}, we see that tan(t) = 32/15 = 2.1333. Thus 2t is about 130 degrees.
The solid angle subtended by a cone with apex angle 2t is 2*pi*(1 - cos(t)) steradians -- thanks Wikipedia. So that's 2*pi*0.58, approximately, and the whole sky above the horizon is 2pi steradians. So the moon should, in this model, take up about 58% of the sky -- just over twice your estimate :)
-Erasmus