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The central question in free will is not, as you maintain, whether or not we have the ability to do otherwise. The central question is whether our actions are up to us -- this is why randomness is incompatible with free will. The question of whether or not we have the ability to do otherwise comes up because it seems like, if an action is up to us, we could have done otherwise. But this definition itself has its problems. In any case, I think it's easier to see how omniscience, which does not entail any influence on our actions, fails to conflict at all with free will. (Whereas Omnipotence might, but probably doesn't, and Providence gets really tricky).
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"Die Deutschen meinen, daß die Kraft sich in Härte und Grausamkeit offenbaren müsse, sie unterwerfen sich dann gerne und mit Bewunderung:[...]. Daß es Kraft giebt in der Milde und Stille, das glauben sie nicht leicht."
"The Germans believe that power must reveal itself in hardness and cruelty and then submit themselves gladly and with admiration[...]. They do not believe readily that there is power in meekness and calm."
-- Friedrich Nietzsche
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