Another obligatory New PM-833TV and PM-1340GT Ordered!

The tool will lift and pull away from the spindle as its advanced forward with the cross slide behavior shown in the last two videos. The amount of pulling away is amplified by the fact that the tool is on a fulcrum arm (compound plus QCTP).
 

They probably watched this, and are starting with the easy things first. I think you are on the path to resolution.

Directly measuring the cross slide ways on the saddle for twist is easy enough using the crossed diagonals 1-2-3 block and straightedge approach from my earlier post. No need to mess with any other aspect of lathe alignment.
 
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Put another way, as the cutting tool is advancing forward it is cocking to the side toward the tailstock, and pulling away from the part that is being faced off.
 
It is possible for the Rollie Dad cutting test to show acceptable results, while in fact the spindle axis is tilted and the bed twisted is such a way that the two alignment errors cancel out each other. This is one reason I align the head first using a precision test bar seated in the spindle MT taper.
 
Have you put the cross slide on a surface plate to see if the bottom is actually flat? If the cross slide itself is twisted, that seems like it would give you the issues you are measuring while still giving you good results when checking the head stock alignment.
 
Good news. The saddle I think its the saddle?) Is ground basically beautifully.


The cross slide seems to be not nearly as good. It is tough to measure with a depth gauge, but I did my best. a good bit of fluctuations at any given position on the scraped bearing surfaces. Did my best. Also did a tap test on all 4 corners on a surface plate. Seems the piece had some stress in it when machined?


 
The tap test suggests that the bottom ways on the cross slide are not flat and coplanar. Do you have a way to measure how out of whack they are? Hi-spot blue, feeler gauges, indicator on a stand to see how much it moves when you tap it?

And at least a cross slide is easy to replace.
 
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I’m sorry to see my suspicion is correct, but on the bright side, your headstock is aligned :)
 
I'd return that machine and get your money back. I went through a similar ordeal with an improperly machined Y axis on my 833TV mill and spent months and hundreds of hours convincing them of the issue. They eventually agreed to change out the mill with a new one and I waited 7 months for that to arrive. When it arrived I made sure to inspect it thoroughly and found the column (nod) was out of square to the table .015" over 10". I sent them a video and their response was simply "I swear they move during shipping". No offer to fix or exchange it. I said i would re-shim the column just to get a working mill, and asked if they could send me some shims. They said they didn't have any and basically sent me to buy shims to fix a brand new (second time!) Machine.....
 
Parts certainly can shift after machining. I purchased a Drill Press and the table was noticeably concave. After several days of trying to level it using sandpaper (I didn’t know about surface grinding then…) I got a replacement part under warranty.

The machining marks on the table showed it was finished by a process which would have been unable to make the table concave, which leads to the conclusion that the part warped after manufacture.
 
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