At least we won’t have to do that any longer.
OK, so the rich Torchwood-fleecers have a device that can repair biological tissue, and they want the Master to fix it so it makes someone immortal. Clearly the way to do this is to have it constantly repair biological tissue, so ageing is constantly reversed, every second of every day. And the Master tweaks the machine so it turns someone into him (well, not him so much as someone who behaves exactly as he would, and will obey the Ur-Master’s commands).
But how does he manage to make it do this to everyone in the world?
The answer is quite simple. The Master’s satellite network, which he spent 18 or so months developing, which he used to sway the entire world to his bidding in the last season finale, and which the Doctor neglected to disable.
You not only have a shout-out to previous RTD Who events, you also highlight the Doctor’s growing (and possibly fatal) arrogance, similar to when the Ninth Doctor thought that shutting down a malign news network would be enough to restore history to how it should be, not thinking about what would prosper in its place (endless game shows and, eventually, Daleks).
Don’t have time for this in the running schedule? Just throw out the stupid Timothy Dalton voiceovers that don’t advance the plot one whit. Show, don’t tell.