Although I really liked the idea of the router jig, I'm not confident that is would hold the tight tolerances I'm shooting for. I decided to turn them on my lathe again but I came up with some ways to make it easier on myself. First I cut my square stock to 27" (2" longer than final length). I rough out the diameter with my gouge and then with 80grit sandpaper. Since I only need the accurate diameter on the last 3" of either end I use my skew to close in on the diameter near the ends. Then I took a 4/4 piece of poplar and got one face perfectly flat on my jointer. I then stuck a piece of 150 grit adhesive backed sandpaper to the poplar and used this flat sanding block to work the ends down to final diameter. The flat sanding block helps to maintain an even diameter unlike a loose piece of sandpaper. Then when I have the ends to the right diameter I just sand the center portion to visually blend without much concern for diameter. It still takes a lot of time but having a method makes it go much better without as many mistakes.
"What we hope ever to do with ease, we must first learn to do with diligence".
- Samuel Johnson