Transcription was so frowned upon in some network circles that even in 1948 -- by which time transcription was becoming fairly common on the networks -- "Escape" on CBS would do an East Coast show live from Columbia Square on Sundays, and then re-do the whole show (at considerable expense) live for the west coast stations later in the week.
Syndicated shows -- on an ad hoc collection of stations, not a formal, established network -- often would press copies probably in the dozens for distribution as you outlined above. I've personally handled and played 16" syndication pressings from as early as 1932 ("Chandu the Magician," I think). Many will remember a Christmas series called, "The Cinnamon Bear," that was broadcast for many years via syndication, usually as an advertising tool for a local department store.
Several years ago, I got to do some work with the 16" discs of the Milo Ryan Phonoarchive, a famous collection of discs donated to the National Archives by KIRO in Seattle. The KIRO discs (all instantaneous cuts) were all catalogued, but many discs from Seattle NBC affiliate KJR had been added, and were not catalogued. (I got to do that.) Every disc that was a network show was an instantaneous cut made in the KJR studio (presumably for time shifting).
I don't know of any network shows that were distributed by sending actual disc copies to individual affiliates in the 1940s. It may have occurred, but I don't think it was standard practice, at least not for major prime-time broadcasts. For syndicated shows, it was de rigueur..