If you have a four jaw chuck you can turn that 20 inch shaft on your lathe much the same way as I contour my rifle barrels. Don't use stock any longer than you have to. You should also turn a bushing for the outboard end of your headstock to prevent whip.
1. Centerdrill each end as accurately as you can.
2. With one end centered in a four jaw chuck and the other on a center in the tail stock, turn about 3 inches at the TS end to your finish diameter.
3. Swap ends and do the same thing to the other end (at the TS)
4. Slide the part into the chuck with about 6 1/4 inches of stickout and put the end onto a live center in the tailstock. You now have 3 inches of finish diameter and 3 1/4 inches of the original diameter showing. Turn down the next 3 inches going towards the chuck to finish diameter. Add 3 more inches of stickout and do it again...and again.
5. When you run out of room, swap ends and repeat the process going the other way, always turning within 3 inches of the chuck until you reach the finish diameter you already turned.
It will come out as good as your ability to center work in your 4 jaw (both for the turning and the center drilling) so use a good indicator and take your time. Because a 4 jaw chuck has so much bearing surface on a part, sometimes a slender part can be bent slightly if you're heavy handed with the chuck and then jamming it into the center. To allow a part to find it's own center without stress, I like to turn a bushing to go on the part that only will have 1/2 inch of bearing on the chuck jaws. It's enough to drive the part but still gives you some wiggle room if you need it. I'll attach a pic of a bushing and a barrel half finished using the above method. This particular bushing is steel but you can make it out of aluminum, PVC, brass or just about anything else. The pinchbolt makes it go quicker but isn't absolutely necessary. A slit will do.
