We don't cover the compatibilism/incompatibilism issue, but for the record we are both compatibilists
The problem here is that Compatibilism, at least of the sort we are discussing, is not actually "compatible" with hard determinism.
Fatalism itself, the language of "must" rather than "shall" in the classic sea battle discussion contains an actual syntax error, where "at the same place and time" is exposed to be as "as nonsensical as trying to "set a non-static member on a static type".
I'm not going to get into that here, but the result is that you just have to flush the intuitions of both hard determinism AND libertarianism, if you want to stay consistent.
The problem is that it just makes no sense to even think that things must be different in the same conditions, when things are clearly different in different conditions. It is the direct demand for a contradiction there.
Moreover, discussing determinism before compatibilism seems to be burying the lead.
When we say "it could be otherwise", in the sentence, the could applies a modal modification to could, and is a necessary operation: instead of looking at the thing, you look at its properties, not the context of it mind you, JUST the thing.
Then you present that thing to a context.
Then you see what that thing does...
The metaphysical function this generates is a mapping of are all the things that model could execute in all the various contexts.
"of all the objects in the universe that have you-property, some of those objects do the thing, even if you did not do the thing" is then an equivalent statement to saying "you could even if you didn't".
The result is to just reject "Hard" Determinism (fatalism) with the same vigor as we reject Libertarianism.
Compatibilists are NOT hard determinists, and hard determinists are NOT compatibilists. The compatibilist says "an elsewhere-otherwise is otherwise enough for 'can'."