Well, I found this comment in Solow's and Justman's book Inside Star Trek: The Real Story:
"Later, while dubbing various episodes, we took reality one step beyond. We rented a special machine that was used to change the pitch of people's voices without affecting the speed of the sound track, thereby keeping the dialogue 'in sync' with the picture. Although the device was large, clumsy to handle, and expensive, it helped make alien humanoids sound as alien as they looked."
So, I still don't get how this 1966 "black box" worked, but I take Bob Justman at his word that there was indeed some large, clumsy, expensive tehcnology available to have changed the pitch of Malachi Throne's voice--and, off the top of my head, probably Cloud Williams' in "The Omega Glory" and Lt. Mira Romaine's in "The Lights of Zetar."
Cool. I figured if it was some kind of black box, it would be some kind of clumsy thing.
I stand corrected. Thanks for the clarification.