Sorry for the late reply, life is seldom as smooth as we would like it to be
Yes, I think there is a pretty simple way to make a conical drill: just make it cylindrical by rotating a suitable profile and then use Dennis' "box conform" plugin (in the 'Tools' menu) to reshape it into a cone.
To do that draw a vertical square-based box and then shrink the 4 topmost vertices to
nearly 0 (but don't collapse them together entirely, the box must still be a box), then call the plugin and follow its instructions.
Easier then you think...
