Years ago I got a couple of used Parlec CAT40/ER40 collet chucks and turned the flange and body into a #4 1/2 Morse taper adaptor for my Sharp 1236 lathe. I did also turn the back end similar to a C5 thread for a draw bar. I will only use the adaptor for light cutting when I don't have a draw-bar engaged to keep it in place. Chatter of any kind can cause the locking taper to fail. The drawbar makes the taper fail safe and allows you to torque the ER40 collets without slippage on the taper. Also, when you have a short part or parts, cut a short blank the same diameter as your workpiece and push it in far enough to support the rear portion of the collet while simultaneously gripping the short end for machining. Typical runout on my chuck/collets on a piece of barstock is less than .001 and I can't tell you if it is the part, the chuck, the collet, out of round material, or my machining job in creating the taper. Most of the time, runout is .0005 or less.
Good Luck!
Gary