Frustratingly enough, I switched to mapping to a cylinder to simplify
matters, and actually got it to work once. When I re-entered my key cell
after completing the animation I noticed that the brush wasn't grouped to
the cylinder any longer….. I thought I had it for a second, but since
then have re-rendered with and without the brush grouped to the cylinder
and I can't duplicate my success. I'll be sending the files your way after
just one more cycle of trying. One thing I did do was to make the brush
axis tangential to the cylinder like this O_ and then wrap around the Z
axis. To me that looks like the way to start the wrap, and I've had no
luck with centering the brush axis in front of the object, or bisecting the
object with the brush.