I think it is possible. Try this: Go to an intermediate frame and change the U value in the channel box (motionPath input node)... I'm just reading this out of a book, so hopefully it works.

Okay,...

It might not only be animation tangents, but the spacing of CVs on the curve, you could try rebuilding curve to see if they space better. All around it's quite strange... it's a mayastery.

Hmm, it's weird, I have no problems extruding along a curve that has been drawn on a live surface. I can also duplicate the curve, make the surface not live, then move that curve around and extrude...

What about extract or something?

If you duplicate the curve (and delete hist), does it then let you do whatever with it?