> Even if Sauron can cause Mt. Doom to erupt immediately, we know from the actual story that the eagles are capable of navigating into Mordor and locating and rescuing Frodo and Sam, despite the major eruption which was taking place. Even if Sauron did manage to catch the eagles in the eruption, however, could this melt the Ring? If Sauron does manage to figure out that the eagles are carrying the Ringbearer, he might opt not to cause Mt. Doom to erupt, just for this very reason.

This suggests a far better option: Sauron could have cooled down mount doom, and then when the eagles arrived there would be nothing they could do to destroy the ring. Meanwhile a massive army from all over Mordor would be building up around them, and the Nazgul would be on their way to capture the ring before they could get out of Mordor. Of course this does not counter the argument that the option was not even discussed.