This catalog dated Sept. 1940, lists only the 3A Series II with only the Anastigmat f/6.3 and Diomatic shutter at a price of $42.50:
This subsequent catalog dated June 1941 also only lists the 3A series II, but the additional supplement in the back dated Feb. 1942 also lists the 3A Series III with the same Anastigmat f/6.3 lens and Kodamatic shutter at a price of $55.75:
The 3A series II has no price listed, implying it was discontinued. Your introduction date for the Series III has to be between June 1941 and February 1942.
It should be kept in mind that the War Production Board was established under Executive Order 9024 in January of 1942, and would prohibit nonessential production with most civilian goods like cameras that were not being produced for the war effort in April of 1942. Thus, the 3A Series III would have had a very short production run even if existing stocks were able to carry sales on into 1943.
I find it interesting to compare relative prices. For a comparable cost as the 3A Series III, you could purchase a Monitor Six-20 or Six-16 with the Supermatic shutter (1-1/400 vs 1/25-1/200 of the Kodamatic) and the Anastigmat Special f/4.5 lens or a Kodak 35 Rangefinder with a Kodamatic and the Anastigmat Special f/3.5.
For half the price of the 3A Series III, you could get a Bantam f/4.5