The only "Last Days" are the last days the 8 members of the Governing Body have left before the die.
That brings up another point - at the same Annual Meeting, didn't Sam Herd speak about how all the "annointed" would have to die before Armageddon? Herd also stated that Witnesses shouldn't be afraid of that because Jehovah would not abandon them. That's code for the "Helpers" will replace the Governing Body.
That leads me to believe that is the Governing Body were to all die in around the same time that the Watchtower would be run 100% by "Other Sheep" and anyone still claiming to be of the annointed would be told they are not. That would have to come about.
I have to believe that one of the reasons for the doctrinal change that only the Governing Body are the "Faithful Slave" is because they do not want to risk other Witnesses who claim to be of the annointed to try and take the reigns. My father was disfellowshipped back in 1992. He was not told why, but I found out from a friend who attended a party in which one of the elders on my father's committee was present. That elder blurted out, "We just had to disfellowship someone for apostasy." No one else was disfellowshipped at the time so it narrows down the who.
At my father's judicial committee he was asked, "As a brother who claims to be of the annointed, do you also claim to be part of the Faithful and Discreet Slave class?" My father answered, "Yes." Keep in mind that this was 1992. The official stance of the Watchtower was just that even though Witnesses tended not to think so.
Sorry to hijack the thread, but I believe this is related to both Herd and Morris' talks at the Annual Meeting.