What you have forgotten( or I think that you have forgotten) is that a lathe is NOT
a trignometrical figure. It is relatively a weak piece of equipment which will bend on cutting loads. If one creates a lathe to follow a pure rectangular shape, the cutting forces will create a convex
shape. It then that this 'rocking about like a pea on a drum' of two convex faces occurs.
Clearly, I have little or no experience of what happens on Andy's lathe but I suspect that much of the problem lies in the lathe being flimsy.
Am I wrong? Well someone in a distant and nigh forgotten past wrote of what happened when he stuck his elbow on the tail stock( bored rigid) during a long cut. Again, Thomas wrote at length about the subject in MEWM and earlier in ME. Tom Walshaw wrote extensively on the subject of lack of rigidity and his lathes constantly having to be adjusted - because of earth movement- in his retirement. Again, he wrote of problems of flatness in single point milling and filled Model Engineer with comments from people- who hadn't his maths skills
However- and it is worth thinking about- I 'did' the history of a chief draughtsman of a then very successful machine tool works. He left a few mediocre watercolours of a few lodges, a church and a couple of Scottish scenes and an engraved silver cigarette case.
In real money, it probably amounts to enough cash to fill a car with fuel-- and his wonderful business is - poof- gone- like him.