I would say this is a job for somebody with a CNC lathe. Do you have such a lathe?
In any case you'd try to automate the whole job as much as possible. Example: cut the two chamfers before you part off the puck. Use the highest speed possible, to ensure you don't need much finishing after that. Use tools with hard tips, so you don't need to resharpen them all the time. And don't do anything with jam chucks and hand sanding. Put as many of the pucks as you can into some sort of rotating drum (a washing machine would probably work) and tumble them, maybe with some material to aid with smoothing the surfaces.
Once you have the process sorted out, you can figure out with trial runs how long each step takes. From there it's a simple case of same basic maths.
As I see it, this is border line mass production, and there are companies who are set up for this kind of thing. Are you happy to compete with them?