I did some research and learned that while Iran tried to remain neutral during World War II, by the time my aunts were attempting to leave, Iran had joined with the Allied Powers, providing an important water and rail supply route to and from the Soviet Union. The suggestion that my aunts return home through Tehran now made sense to me.
It is important to note that two letters which I found at the National Archives validated their American citizenship and acknowledged the passport applications which they all executed on April 9, 1940. In fact, a letter from Charles Dickerson, chief of the consular section in Kuibyshev to the Assistant president of the Kuibyshev Executive Committee informed him of their status. Mr. Dickerson also asked the Soviets for assistance in finding the girls temporary living quarters.
On the surface, this sounded as if their departure would be relatively soon, since they now had a travel route out of the USSR and the support of the American Embassy. Unfortunately, this was not the case.