@opensourcefan - your thread came off the rails a bit there and I apologize for my role in that.
I confess that I am a bit confused. I re-read your entire thread to try and make sense of things.
Normally, when a lathe produces a taper that close to the chuck, it is not the Chuck's fault unless the chuck is loose. No matter how badly a part is held in a chuck, and no matter how badly the chuck is attached to the spindle, and no matter how out of round the chuck is etc, the part will turn concentric to the spindle, not the chuck. A better chuck will only help hold a part more closely to the axis of the spindle.
In my mind, there are only three possibilities.
1. The axis of the spindle is not aligned to the axis of the bed.
2. The tool holder is moving up/dwn or In/out while it moves on the bed.
3. The chuck or the part held in the chuck is loose and moving around.
I expect this might sound like Greek to you, but think about it. With a good lathe that is setup properly, and a really crummy 3 jaw chuck, you can put a chunk of square stock in the chuck, and turn a perfect cylinder with no taper. When the tailstock is not used, tapers at the head only happen when the spindle axis is not aligned with the axis of the tool travel - which should be the same as the axis of the bed.
You cleaned up that chuck and I think it's probably ok now.
But I don't think your head and/or ways are aligned properly.
I confess that I am a bit confused. I re-read your entire thread to try and make sense of things.
Normally, when a lathe produces a taper that close to the chuck, it is not the Chuck's fault unless the chuck is loose. No matter how badly a part is held in a chuck, and no matter how badly the chuck is attached to the spindle, and no matter how out of round the chuck is etc, the part will turn concentric to the spindle, not the chuck. A better chuck will only help hold a part more closely to the axis of the spindle.
In my mind, there are only three possibilities.
1. The axis of the spindle is not aligned to the axis of the bed.
2. The tool holder is moving up/dwn or In/out while it moves on the bed.
3. The chuck or the part held in the chuck is loose and moving around.
I expect this might sound like Greek to you, but think about it. With a good lathe that is setup properly, and a really crummy 3 jaw chuck, you can put a chunk of square stock in the chuck, and turn a perfect cylinder with no taper. When the tailstock is not used, tapers at the head only happen when the spindle axis is not aligned with the axis of the tool travel - which should be the same as the axis of the bed.
You cleaned up that chuck and I think it's probably ok now.
But I don't think your head and/or ways are aligned properly.