The parts probably look something like this after the lathe OP.
My first thought is that you might be able to get away with screwing them into a fixture plate. The parts will cinch-up against the mating surfaces & if your CAM program makes all it’s cuts such that the forces are all clockwise that might be enough that they stay put. Otherwise, the plate would need some more features – not too difficult…
Yeah, I see your OD is 29mm and that’s not going to happen with a 5C collet & bar puller. I think the max here is 1 1/6” or about 27mm. With the 3-jaw chuck on my Slant-Pro I can get 1.5” through the spindle. Unless you can make your part a little smaller OD wise you would have to use the 3-jaw chuck and advance the bar stock by hand – at least on the Slant-Pro. There are machines with hydraulic chucks but they’re pretty expensive.
I’m not a fan of the Rapid Turn concept. Just too much work to switch back & forth.
I think it’s doable and that’s why I have a few machines. It’s costly to make prototypes and small lots and that’s where these hobby machines come into play. I’m retired (don’t have to work anymore) but I still like making things.