From what you have described, it may well be that your headstock is pointing slightly toward the rear side of lathe. That was my measurable conclusion (starts about post #17).
http://www.hobby-machinist.com/threads/tail-stock-alignment.53621/#post-446343
Traversing across the chuck face should theoretically tell you the same thing, however its a shorter distance so more prone to error measurement. It also presumes chuck face is ground perpendicular & sitting 100% accurate on spindle nose etc. Maybe facing off a face plate & measuring dish or V might be more indicative?
I just received a precision ground test bar, MT3 on one end, ~8" constant diameter on the other. Its supposedly very accurate ...if I believe all those 0.0000 zero's in the ebay advertisement from India
My lathe headstock is MT5 spindle & it came with a ground MT5/MT3 adapter sleeve. I dry assembled the parts & they stuck like glue so I'm going to install the assembly & traverse down the ground surface bar sticking out with DTI. No chuck or tailstock involved. If that confirms the same taper amount I last saw from my last cutting test, I think this will be a good & quick way to check validate the lathe every so often. MORE often! Its probably not a replacement for actual turning test, but I also think turning can introduce some degree of ambiguity depending on material, diameter, cut, cutter, unsupported length, diameter measurement etc.
Personally, at least after my own experience, I think this whole lathe jacking thing should be the second thing not the go-to initial fix. For sure the lathe should start out level (meaning without twist) with best instrument you can lay hands on. But a likely culprit is headstock rotation & it only takes a smidge to achieve taper. That was also how the story ended in the 2 YouTube videos I referenced in my post from pretty experienced guys. Put another way, if lathe bed was actually 100% level (non-twisted) & unbeknownst to you the headstock was the culprit, then shim jacking the lathe bed to impart compensating twist now means you have 2 problems fighting one another, not just one root cause. And its probably not doing the bed casting any favors either being twisted outside of how it was initially ground.
After adjusting mine back I've also been wondering about the set screws that adjust the head in position prior to locking down with vertical bolts. I kind of viewed them as jacking screws t assist rotation which is probably what they are. But if for whatever reason they backed off or loosened on their own over time, then thousands of repeated cutting pressure traverses might slowly serve to swivel the headstock over time? (viewed from top). Who knows on that one, but I would for sure check after moving the lathe. I'm still not finished my alignment tune up but now I'm glad I have at least an appreciation for what's going on.