I like to think that we're all time travellers, collectively collapsing the universe's wavefunction through will alone... And now I'm onto determinism so I'll shut up.
I like that. Though I would think it is not 'will' but 'life' that interacts with universal determinism, through physical expression of information over time. How that information will express itself (how gene-information will translate into physical realities in each moment) seems in the realm of the unknowable (like turbulent flow or other instances of Lorenz-y chaos in the Universe), and consciousness as one of those gene-expressions makes this even more loopy.
But I've wandered into Leary-esque fascination with faults of perception lately, which ought to stick to the human-describing world of psychology, so I should probably shut up too.
A new-reality model of time travel only affects the viewpoint of the time traveler.
Likewise, lots of time travel in fiction actually has the hidden assumption of a second time dimension. If a second time dimension existed, causality could be maintained along that dimension while seemingly broken in the time dimension we know and love.
And there's always the possibility that causality isn't a given and is simply how we experience the universe. Just because it has always been observed and it makes intuitive sense doesn't mean it is always true. :)