OP here, yes, good write up, although I wish someone would code up a simulation that showed it and allowed us to hear what this telephone sounded like to FDR and Churchill.
(I see now that it was already linked elsewhere in the the thread.)
Pretty impressive for cross atlantic one-time pad voice comms in an analogue era, I think. It's amazing what money and smart people can accomplish.
Also found this fantastic page: https://www.cryptomuseum.com/crypto/usa/sigsaly/