Btw, I’ve been using the longitudinal/ crossfeed lever, not the long lever. I reserved this for screw cutting
I feel that is where your problem lies.
Based on the way the gear train 250, 280 and 290 machines work then the lead screw also acts as a feed shaft, You should be familiar with industrial machines that have more than one shaft across the front – a lead screw, a plain feedshaft with a keyway and a control shaft.
The “feed lever” on the front of the machine takes the drive from the keyway and through a set of gears and either moves the carriage via a pinion that engages with the rack on the front of the bed or by another set of gears drives the cross slide lead screw. In both cases the thread and therefore pitch of the leadscrew does not really come into play and those internal apron gears will reduce or increase the number of handwehel turns relative to the feed slots rotation, usually giving a finer feed per spindle rev when facing to turning*.
For the Auto turning (lengthways) to work correctly the Leadscrew thread needs to be used so the half nuts need to be engaged, backlash taken out by using the electronic feed to move the carrieage, tool position set and then the cut made.
* I suspect this is why you first got the incorrect movement as the feed shaft driven gears within the apron move the carriage at a different rate to what a leadscrew would move it. So the 2mm pitch that was set at the factory may well be right. Reducing the pitch setting actually just reduced the error.
My suggestion would be to check that the pitch is set correctly is to reset the leadscrew pitch to 2.00mm in the settings. Engage the half nuts and move the carriage to the left a little. And take a measrement of it’s position from a fixed point. Better still if you have a plunger type indicator then move the carriage upto that and set the dial to zero. But make sure you are only moving the carriage to the left which eliminates any backlash.
Then use the FN key to select “automatic turning” and follow the prompts to set a known distance say 10mm or 12.7mm if using imperial measuring tools and to “stop” at the end not return. Then start the spindle turning and click run. The carriage will move to the left and stop at the set distance. Measure how much it has moved and report back. If all is OK I’ll explain how to make cuts using teh feeds, if not we can look again at the numbers.
This should give you an idea of what to engage and what buttons to press. As I was using an imperial gauge I set the distance to 12.7mm (0.500″) and got five turns of the dial at 0.100″ each.