I mean, think about it for a second. You have a choice between A and B, and you freely choose A. From your definition it seems that if I rewound time to that moment, you might choose B instead. But it's the same situation! If I freely choose to take a walk this morning because it's nice out, I goddamn mean to go out. No matter how many times you rewound time, I would want to go out every single time. It isn't random: there's a reason why I'm doing this, and reasons are never random.
If free will is nondeterministic or random, then I don't want to have free will.
The key difference is whether that reason is entirely internal to you or it's the result of external influence. If you always take a walk, an observer could infer that by some arcane law of physics, the sun forces you to take the walk - and they might not be far off.
What I mean by nondeterministic/random is there is nothing someone could know about you, the sun, and the rest of the universe that would let them predict with certainty whether you'll go for a walk or not.
The supernatural ability to rewind time seems like cheating, to be honest. But if that were possible and everything always went the same, then perhaps we could rule out free will (depending on the nature of this time reversal mechanism).
Nothing someone could know about me? If someone knew everything there is to know about me, I sure hope they would be able to predict everything I will do. Free will doesn't mean freedom from my own nature.
The only way to be perfectly unpredictable is to act at random and without reason. If you act for a reason, then in principle, that reason could be known by someone else, and they could predict your actions. I think that's acceptable: I don't feel that in order for my choices to be free, my nature and my reasons must be unknowable to anyone but myself.
> But if that were possible and everything always went the same, then perhaps we could rule out free will
According to your definition, yes. Not according to mine. So I guess we made the OP's point ;)
It's more difficult if we have to consider the internal, subjective state of the system. A radioactive particle probably doesn't experience anything we could identify with when it "chooses" to decay. And the experience we imagine to be free will could in fact be entirely deterministic, even if other aspects of the universe are nondeterministic. But if we can rule out any kind of nondeterminism in the universe, then we can rule out free will.