and time lords don't age, so how could it work? Could it work at all?
yes they do. there was a bunch of old Time Lord dudes in "the deadly assassin," including the OLD retiring president.
and all some badie needed was a machine that messed with the docs time lines and aged them [by draining their life forces ???], something along the lines of a machine like they have already established as cannon. like the one in "the leisure hive" perhaps?
all very simply explained actually.
and near the end of the story, the machine would appear to have a reverse mechanism, and matt smith's doc would be the first doc restored; and then the episode would end as matt's doc steps out of the machine's field and says: "next?"
and at the point, we would know everyone else was going to be likewise restored, and returned to their correct Time Streams, in the correct age bodies.