OK. So, do you consider that you actually have good evidence for the existence of free will in this sense? If so, what is that evidence?

The obvious alternative hypothesis, which seems to me to explain all the evidence I know of just as well, is that at the level of physics there's nothing but determinism and maybe randomness, but it looks different to us because we can't see all the details. We think "I could have done otherwise in the exact same situation" because we have seen ourselves and others do different things in very similar-looking situations, we can imagine making a different decision in what feels like the same situation, etc.; but we don't get to observe the exact states of all the particles that compose us and the world around us, and what we think of as "the same situation" may actually be quite different in its details. We also don't get to observe the mechanisms that lead to our making whatever choices we do, so those choices feel like opaque black-box miracles to us. No magical contra-causal free will is required for things to look this way to us.