This is not so much a theory, but more what I would do if someone were stupid enough to let me write Doctor Who.
The TARDIS team are all worried about starting off a paradox, but there's already one in action and all of the Future-Doctor's manipulations are aimed at fixing it. The astronaut on the beach in 2011 is not the same one we see in 1969, and it's the Doctor himself under that helmet.
(This is a theory based entirely on that one scene where the Doctor puts on an astronaut helmet and claims it's what "cool aliens" would wear. I think this is foreshadowing from Moffat.)
So the Future-Doctor is, by a work of cosmic irony, a product of a paradoxical timeline caused by the TARDIS crew trying to save the Future-Doctor's life, and in order to stop the paradox, the Future-Doctor has to die. Who better to do that than the Doctor himself? After all, as River says in a different context, who would you trust above all else to undertake such a task?
(This is also more or less the plot of Donnie Darko, but anyone who's read The Time Traveller's Wife knows that Moffat is not above borrowing from other sources.)
I do wonder if it's River under that visor, and if her killing of Future-Doctor is what has her incarcerated in Storm Cage, but that little throwaway scene with the Doctor wearing the astronaut's helmet strikes me as significant, in much the same way as that bit in "Flesh and Stone" where the Doctor comes back to Amy shortly after leaving her in the forest and begins speaking to her out of context. I knew there was something off about that bit, and I was proved right; I think the helmet scene will be much the same, and if I'm right, it suggests that the Doctor strikes the killing blow.