Terminator 2

[A Black Falcon]

I'd typed a reply yesterday, but the downtime earlier wiped it out... :(

But how about 'the past is unchanged, but the future is now different'? That's what T2 chooses as a timeline design, after all. It's not one of your four choices, but it's what they do... couldn't-have-existed-now robots and all. They were sent back by the future that had existed, after all... evidently in Terminator timelines changing history does not change the past or the present, just the future. Perhaps it's a splitting timeline thing, where there is now another universe where things went differently, but they never implied that it was even that... just that it is now different. It's not a paradox, when the robot was sent back it existed, and when it was in the past it was there, even if later events made it impossible for it to have been sent back... it was already in the past, that event happened.

You're right that with time travel saying such things is dangerous, because if you just skip around (in time) that whole thesis could fall apart into incoherence, but as far as they took it, at least, it worked.