Let's close out further speculation in this thread.
It's clear that many in the service liked the Air Corps name, and may have preferred it. However, after March 1942 the Air Corps existed only as a subordinate element of the Army Air Forces where it organized training and support commands. The Office, Chief of Air Corps was abolished and these components reported to the Chief of the Army Air Forces
1.
I think we need to also recognize that the service went from some some 21,300 personnel in 1939 to a peak of 2,411,000 in March 1944
2. That's in addition to employing up to 422,000 civilians
3. It required a lot of reorganization and change to accommodate this amazing growth.
I don't suspect that sending out memos on how personnel were to sign official documents was very high on the priority list.
What is clear that the confusion was done away with by the National Security Act of 1947.
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1 The Army Air Forces in World War II: VI Men and Planes, edit by Craven and Cate, p. 31.
2, 3 Ibid, p 32