But that's my point – the standard philosophical definition separates the existence of choice from the question of whether it is free or unfree – but you aren't using the standard philosophical definition, because you are conflating those two issues.
And you aren't using the standard common sense definition either – for, surely per the common sense definition, this is true: "I can choose what I eat for breakfast, but I can't choose what Donald Trump eats for breakfast" (because the first is clearly within the scope of my own personal causal power and influence, the second is well outside it) – yet by your own definitions you'd have to reject that statement, and say "no, you're wrong, you can't choose what you eat for breakfast" – whereas most incompatiblists would instead say "yes, you can choose what you can eat for breakfast, and you can't choose what Donald Trump eats for breakfast – but your choice of what to eat for breakfast isn't free"
So I'm using the word "choice" in the standard way, and you're using it in your own personal idiosyncratic way