Part of the problem and maybe the solution lies in your motion control software. There is usually a "CV" (constant velocity) setting. If this is turned off, the machine will stop at every change of direction and then restart. With it on, the machine tries to keep up a steady cutting speed by very slightly (and generally imperceptibly) rounding off the "corners" but giving a much smoother motion. Much smoother! Anyone who has been through this will know what I mean! This explains why straight cutting is fine but highly-faceted cuts are not.

This also helps the quality of finish doing the kinds of thing you are doing. I've just finished a project which involved copying a 3D relief carving by measuring the original across a 1mm grid and converting the mesh into a highly-faceted model and hence toolpath. However, using the appropriate CV setting I have a very smooth finished result. I also used vCarve for generating the toolpath although my mesh model came from other software. However, I would expect F360 or any other CAM software to do the same thing - it's generating a toolpath to match the model and the answer is at the motion control level.

Good luck!