production is large-scale and gets noticed, even when the producers would prefer otherwise. There's no way for Gatiss or anyone else to be filming or even preparing to film the show without fans and/or the media finding out about it. At this point, with Moffat still (per the costume designer) working on the script, they're going to be rushing to start by the announced late March/early April date, not looking at secret filming before that. Unless we're to assume that he's finished the secret
script, which is being worked on by the secret
costume designer, and somehow filming alongside An Adventure in Space and Time
without any of the people who are taking pictures of it noticing...
I appreciate the desire to imagine ways in which there could be more than ~120 minutes of Doctor Who
being made for the second half of 2013. It still baffles me that they couldn't pull together something more than that. But there's no sign of it happening, and given the time-scale on which the show is made, it's already too late. If they were making a second anniversary special to air before Christmas, they'd be doing it before Matt Smith's three-month break, not after. Because there's no way a substantial portion of the anniversary is going to be done without the current Doctor.