teilhardo
One trick you could use would be to undercut the flutes of your tool to give it clearance so that the whole depth is not engaged.
If your cuts are only .04 deep, then that is really the entire useful length of your tool flute anyways.
Or, you could carefully create some offsets at each new Z level, that would give more clearance to the tool, in effect cutting a tapered wall. The amount could be only .0005 per level or so, I suppose.
Also, make sure to go around at least twice at each Z level, to ensure that all the material has been removed that is supposed to be removed, but because the cutter deflected, it left a bit. This would eliminate the tendency of the tool to "bite in" anywhere.
Climb mill also, to keep the tool from wanting to pull into the workpiece.
Use a tool radius that is smaller than any internal corner radius of your part. You want the tool to never nest perfectly in any corner, rather, you want it to interpolate the corner by swinging through a small arc.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)