This makes perfect sense because in threading mode the carriage is now being traversed entirely by the lead screw acting on the half nuts which are now clamped over the lead screw threads. In this mode you are 100% disconnected from the power feed driveline. The PF rod is just spinning & idler turning certain apron gears but not acting on the apron gears that impart motion to carriage (essentially same as your carriage hand wheel). Actually not quite true - if the PF shaft is horribly bent out of shape, it can still adversely impart an undesirable superimposed finish on top of threading if its severe enough as it sees irregular resistance.
With power feed mode engaged, the half nuts are prevented from closing as safety mechanism. Now the opposite occurs - lead screw is just idling & the PF rod is entirely displacing the carriage so any bends or gear issues will show up in your work even more acutely.
My own personal theory on these offshore machines is that even if the lathe didn't see abuse like lifting straps on the rods, the milled longitudinal keyway slot probably sets up a situation where the steel probably wants to stress relieve itself over time. It may have started life axial but could 'go banana' after a few years even though its semi contained within the carriage mechanism. Maybe if they post heat normalized it or chose a stress free alloy that would help matters but I don't think we are getting that for the cost. The reason I say this is I have read articles where people buy a perfectly straight piece of shafting as a replacement, mill the slot themselves (because of metric key in the hardened worm gear) only to watch their own shaft bow on its own after a while.
Did you happen to notice if your run out was in the same plane as the key slot? I mapped mine down the length of shaft, it was predominantly inline with slot, but also had kind of a helix to it.
Hope this helps, good luck.
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