There's no hidden Doctor beside the War Doctor, they're just counting Tennant's aborted regeneration into his severed hand as one regeneration among the 12.
Oh, by the way, apparently there was one episode of I don't remember which Doctor that showed him playing a "mind war" against some robot thing that showed his previous faces up to Hartnell - and then some more, like Hartnell wasn't his first face (I think when I saw it on Youtube I counted 8 different faces including the known ones). Maybe that'll play a role, or maybe it was forgotten and ignored.
If I struggled to the end of my determination, to the end of my way of life with my followers, if the result is ruin, then this ruin is inevitable. Grieve. Shed tears. But you cannot regret.