When I built my single I hit the same problem. Even if the hole in the cylinder is perfectly straight the thread pulls the shaft off square when the thread bottoms, at either end.
I put a piece of 360 Wet or Dry between the standard and the cylinder (a little hole for the shaft, and I had finish milled the standard and drilled the hole in the same set-up) and turning the cylinder by hand seated the cylinder. Some 660 paper finished it up.
Chuck up the cylinder by holding the shaft and turn the lathe by hand. You'll know soon how square the shaft is!
Hope this helps,
Pete