Hi Justin !

Have you tried to randomize spherical instead of cartesian coordinates?
In this system a point on a sphere (or a direction vector) is described by
two angles and a radius.
The angeles are called theta and phi, one meaning the angle in the xy-plane
(0..2pi) and the other one denoting the angle out of the plane into the z
dimension (-pi/2..pi/2). There seems to be confusion about which letter
denotes which angle.
Read more at http://mathworld.wolfram.com/SphericalCoordinates.html.
There you can also find the formulas to convert a direction vector in these
coordinates to the one you need (cartesion x,y,z...).
Please let me know if that yields a better distribution...it would be of
interest to me

Norbert

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