There's only so far you can go in getting that lash cut down. Adjusting the gibs tighter just makes for stick-slip and that's even worse. There might be a little slop in the screw mounts and I'd look for that (bearings not completely seated and can move in and out a little). If you can get it down to 0.001 that's pretty liveable even without comp but really doesn't seem excessive to have 0.002 or 0.003". Have you tried backing down accelleration? Not sure in Mach but in general controllers will accelerate 1.5 to 2 times as fast to take up backlash as it is presumably almost no load on the motor to do that and it gets done faster. Might be that your accelleration is already high but crosses the line when it gets ramped up higher to take up the lash.
Just a straw to grasp at.
CNC: Making incorrect parts and breaking stuff, faster and with greater precision.