About the RCA Theremin sound a lot of philosophy exists. Good analysis was made by Mike Buffington, RCATheremin.com, mentioned already twice in this thread. Also german Alexander Klaus, Aetherwellen-musik.de, got to the bottom of this sound and timbre.
I attempt to re-create that old sound with a new concept, based on transistors. Here my video about.
RCA Theremin sound re-creating
Hope it's of interest in this theremin community here.