I would use a lathe. The only thing I can not figure out is how to make the fly cut out. How is that done? Chase it with a die sinker's chisel or carbide bits in a dremil?? I can not envision a milling cutter small enough.
I use my drill press which has a rotary table with a small vise and have a fixture to hold the tumbler.
I use a 3/32 diameter 2 flute stub end mill and set the depth of the cut with a special .078 thick gauge
with the depth stop built onto the drill press.I also use 1144 stress proof steel which machines very well
and I run the drill press wide open over 4000RPM if I remember right.I have used this method for over 50
years and I know it works. This is a heavy old drill press and the rotary milling table is an old American
Chicago Tool& Engineering that was made long before anyone went to China with this stuff.
I paid $164 for the drill press new in 1964 and then went Sears and paid another $100 for the rotary
table.Today that table is made in China and is over $700 and that drill press isn't available.
Bob Roller