Decidability of bitstring languages with no ones' complements
I don't think there exist recognizable-but-undecidable OCA languages, because if we have a Turing machine M that recognizes a given OCA language, then we can create a derived Turing machine that incrementally simulates M on both its input and its one's-complement (flipping back and forth, trying a finite number of steps in each simulation) until one input or the other has been recognized.

(Note: the derived Turing machine will also need to be given specific logic to decide the empty string; but that's obviously possible to do for any given language.)

Therefore, you can't construct any reduction mapping that would let you prove the existence of recognizable-but-undecidable OCA languages.