I can choose to do a thing that I neither want nor have to do. I can also choose to not do a thing that I want or need to do. Can I prove that to you though? Does my desire to be contrarian countermand my free will? It very well might.
I can rewind a video and watch it again. That is no different from your time travel example. I don't think we can convincingly argue either way if a quantum field collapse will always happen the same way, even if we were to start save-scumming reality. I kind of hope we will never be able to.
None of this precludes me from having free will in the present. I don't even think I need quantum dice contently rolling around in my consciousness. Even if I am completely deterministic, I can still make choices. My brain is a computational device made of meat. I can only have so much faith in what a choice even means, but I sure think I know one when I see one.