If the chuck grip is suspect, how about this?
Very firmly grip a piece of large diameter bar through the full length of the chuck jaws, and bore it to suit your test piece.
Mark for No.1 jaw, remove and saw cut along vthe length to use a s a collet.
Replace in the chuck. Fit the test material and grip firmly.
Then turn, as the Myford "cotton reel" method, This will tell you if the lathe bed is twisted (If it is, it will turn a taper )
The Myford instructions will tell you which point needs to be raised or lowered to remove the taper.
Ideally, raising blocks provide a screw adjustment to be made, which should aid the process.
Keep on doing this until the test piece is the same diameter at both ends. The lathe bed should now be free of twist.
If tapers persist, you have eliminated one source and can pursue other causes, such as bell mouthed chuck jaws, badly seated chuck, etc
Howard.