Very nice write up, thanks for sharing. I understand the desire to make it as accurate as possible as a goal in itself. From a practical standpoint, if I have a taper of a mil or 2, I hit it with a file. By the way there are special long angle files made specifically for lathes that work better. Also turning between centers or with a steady rest.
If you did need to stiffen the cast iron legs you could bolt diagonal braces on, the bolt holes are typically made a little oversized, torqueing down the nuts clamps the two parts together. Not really sure that is desirable or necessary as even a very rigid cast iron tool will bend and twist a little over time. Also it messes with under lathe storage.
Flex of your test bar (or chuck jaws) under cutting loads can easily cause a tapered shaft, 1" dia by 5" or 6" long. I think very sharp HSS is a good idea, make sure GIBs are adjusted, well oiled, make sure compound rest and cross slide screws were last turned inward. If cutting forces are part of the confusion I think you will typically have a larger diameter further from the chuck. Aluminum will have lower cutting forces than steel.
Consider getting a test bar that fits in the headstock taper. Or use the dumbell you have made and use a test indicator on it as the saddle is moved back and forth to more quickly see the effects of changing leveling up and down with no cutting force. Having leveling feet that can be adjusted will be way easier than shims, I suspect these could be at the floor, adjacent to the rollers or between the lathe and table. I think being able to adjust the headstock relative to the bed could be a huge advantage, on my lathe it is machined to fit so not easy to change if its out.
For leveling the lathe there are different ways to attack it. 1) Adjust it so it cuts strait who cares how level. 2)Adjust it level to the original machined lathe datums, need to find surfaces on your lathe that are not worn. Or as navy chief suggested use the top of the saddle which adjusts it level based on the existing possibly worn V way surfaces. If I were adjusting to cut strait, I think I would record how far out of level it is so I could adjust it back if the lathe is moved.
or when I come down to earth with chasing zeros.
