it is not likely that time-turners would use information-theoretic meanings of 'information' to prevent paradoxes

Ultimately, I agree. The characters say that you can't send information back more than six hours, but that's because of the limits of their understanding. Otherwise things are too rigid. But this thread is basically premised on taking the characters' understanding at face value.

it's most likely that time-turners simply cannot create causal chains where the effect precedes the cause by more than six hours

If you're using an information-theoretic definition of ‘causal chain’, then this is no different!