I watched your part 2, and part 3, then just finished watching "Making a backplate for my metal lathe chuck".
I'm amazed that your runout is so darn good. Appears your tolerance is all with the tight thread fit.
I'm still of the school that believes the spindle pilot is needed to make the chuck concentric to the spindle, as most thread fits are loose. I don't know why you found your chucks not to have this pilot used for chuck concentricity.
I didn't see the brand of the chuck you acquired for this 'upgrade', but it must be pretty good to have such a small runout. I've not purchased an import chuck in a long time, but the few I've gotten had horrible runout. The chucks that came with my China lathes all had horrible runout.
I found the limits of a series 400 QCTP when I did some trepanning operation a few years ago. I was using 1/2" tool bits. When it grabbed, it over powered the wedge clamping action of the tool post, and bent the height adjustment screw over, as well the tool bit, which was a brazed insert type that I modified from a type "D" square insert shape. That was on my big 18x40 lathe, which is all geared head (7.5HP motor). I was hogging out the material in a large steel piston I was playing with for a project never completed of a Stirling engine.

I thought you indicated that you have a rotary table, but surprised you did not use that for the bolt circle drilling of the mounting screws for the backplate. I don't have a drill attachment for the lathe, seems that could be a good tool to make. But then I'd have to make the index for the spindle. I have a que of too darn many projects sitting in the shop.
One of the most useful lathe mods I did was putting a power feed on the tailstock. I have this on my 10x20 lathe, and need to make the same modification to the 18x40. It allows very slow feed using large drills, and they don't grab (I can adjust the feed speed to get the thinnest of swarf from the twist drills), as that was a problem with hand feeding, at least for me. This reduced the number of drill changes or boring bar cuts when enlarging a hole in the job.
I just subscribed to your channel, stay safe in the shop.