I finally sold my Sherline lathe, my first machine tool. I could do this because I have made enough upgrades and fixtures for my newer minilathe to produce all reel parts with just it and my mill.
The last consideration was making a thin (.110 inch) disk as the blank for the front end ring. To do this with the Sherline lathe I bought soft jaws for the 3 jaw chuck. The jaws step was .080 inch and that was enough to firmly hold the disk.
More about soft jaws at this post: Custom Jaws.
This would be a good solution for the minilathe also, but there seems to be no source for minilathe soft jaws. I found a good article on DIY soft jaws: Harold Hall’s Soft Jaws. But I did not pursue this because it appears to require a surface grinder.
I had made a similar spider to use with the Sherline 3 jaw chuck, but it was a loose part in the chuck-spider-work assembly and did not work very well (i.e., disk sides did not come out as parallel as I wanted). The improvement here is a draw bolt to keep the spider firmly against the chuck face.
To make the final facing cut on the spider, I removed the chuck jaws and held the spider against the chuck face with just the draw bolt.