Nice job, Greg.
I can see where you are going now.
As far as backlash is concerned, I don't know if Andrews program keeps the axis as a rotary axis or converts it to a linear one.
If it keeps it as a rotary axis, then I cannot see you having any trouble with backlash compensation, since it clearly auto compensates for the diameter you are working at. The "thrust" of the tool will be taken by the gearbox, and if it reverses to "write" the other way, backlash comes on first and takes up the movement.
I wish I could get down to 4 thou of backlash - I dare not tell you how much my lathe has ( I am working on it, with new ball type leadscrews on the horizon) but I find Mach 3 compensation both accurate and reliable (although to listen to it working is sometimes a bit concerting. I was cutting brass handrails - a pole with a ball at the top and centre and half ball at the bottom - something you cold not do manually - as the z axis came to the ball, the x axis had to come out and back, describing the arc. When it changed direction at the apex, you could not see any distortion in the brass. This, I thought, was excellent.
Best of luck.