Hello again Justin
I spent a pleasant afternoon trying this out. I assumed the units on your drawing were mm. My apologies for the poor quality video: all I had available was a cheap webcam.
The run time for the program is 88 seconds. One could probably get close to a minute with more aggressive roughing and better optimization of toolpaths.
My first tries resulted in a lot of tear out and quite a poor finish. This was with a 60 degree threading cutter, minimal rake, as is used for metal, and a continuous right to left finishing pass. So I thought back to my childhood, when I spent hours watching my father at the lathe. He was a master wood turner, a veritable human CNC machine. He worked for a furniture company before mass automation, and could turn endless duplicates by eye, with only occasional checks with the calipers. I tied to duplicate his movements and the way he held his chisels, ground a 1/8 inch HSS toolbit, mounted it with as much rake as the Sherline toolholder would allow, changed the direction of cut, and got a substantially better finish. The samples in the picture are straight off the lathe, without sanding or hand touch up. One is walnut, the other probably birch. I expect that with additional tinkering with tool angle, feed and spindle speed, it could be better yet.
The workpiece is being held in a three jaw Taig chuck with soft jaws bored out to hold ~3/4 inch round stock. This gives a large clamping surface and holds wood very securely. Mine are bored to maximum depth, though I think that for these pieces, half that distance would be enough and leave you with less waste. I"d be reluctant to use the stock Sherline chuck for wood, the clamping surface is very small and you'd risk spitting the work piece. Taig also makes a four jaw scroll chuck with soft jaws, which would allow you to start with square stock. If you do go this route, (Taig chuck on a Sherline lathe), be aware that the first few threads on the back of the chuck are cut back, and that for full engagement of the threads you need to bore about .1" of relief from the back of the chuck.
Some other details: The control software is EMC2, highly recommended. Gcode for roughing was hand written. The finishing path was traced from your sketch in Coreldraw, exported as dxf to CamBam, which converted it to gcode in the XY plane (CamBam doesn't "do" lathes); then a simple search and replace to change all Ys to Zs in text editor. Finally, a bit more hand editing such that finish cuts are always with the tool moving into the workpiece. Very circuitous, but it's what I have and doesn't take nearly as long as it may sound.
Front and back tool holders are good option on a lathe if you don't have a tool changer. You could mount a roughing tool on one side, and a finishing/parting tool on the other. You may need to modify existing tool holders or make your own to get the correct rake for wood.
Regards
HR
Out of curiosity, what are these for?