Okay, this thread is necessarily very speculative. Look at all that has happened in the last thousand years! How can we even imagine what will happen in the next few billion years? I'd give us a much better chance than that, but it's hard to know.

With the rate that technology is progressing, I'm sure we could make the technology to do almost anything - it's just a matter of whether we'll have it before a potentially apocolyptic disaster occurs.

Most likely, the human race will slowly or suddenly replace itself with bio/machine hybrids to achieve virtual immortality and other enhancements. So perhaps humans wouldn't exist in the same form. By the time the time the sun becomes a red giant, I'm sure it would be rudimentary to be able to change the orbit of a planet.