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determining their absolute , unmeasured trajectories through absolute space
That is irrelevant to a Bell test. In a Bell test, the two basketballs would always be fired along the exact same, known trajectory, in exactly opposite directions.
The whole point of the tests, is that the two Basketballs are also spinning - in exactly opposite, but unknown, random orientations. Your job, is to determine the unknown orientation of each ball's spin axis (either "up" or "down"), in 3 dimensional space, and then correlate one ball's orientation measurements, against the other ball's orientation measurements. The whole point of the test, is to demonstrate that "quantum" objects, will not exhibit the same correlations, that basketballs do.
My point is: Basketballs are not the only type of "classical" objects existing in our universe. Coins also exist. And if some coins are "manufactured" in accordance with Shannon's peculiar recipe, for one single-bit-of-information, then unlike basketballs, those coins will exhibit the same correlations as "quantum" objects.