Nicely done Russ!
There is a technique you can use that turners use quite often.
Put a piece of wrapping paper (or a paper bag works well) between them with some glue. That will hold them together nicely while turning yet allow them to be split apart easily when finished.
I really like your disc technique and I am going to put that in my bag of tricks for plain old turning.
Low Profile CNC Router Vise