In this work, we propose a zero constellation for binary modulation on conjugate-reciprocal zeros (BMOCZ), called jutted BMOCZ (J-BMOCZ), and study its application to non-coherent orthogonal frequency division multiplexing (OFDM). With J-BMOCZ, we introduce asymmetry to the zero constellation for Huffman BMOCZ, which removes ambiguity at the receiver under a uniform rotation of the zeros. The asymmetry is controlled by the magnitude of "jutted" zeros and enables the receiver to estimate zero rotation using a simple cross-correlation. The proposed method, however, leads to a natural trade-off between asymmetry and zero stability. Accordingly, we introduce a reliability metric to measure the stability of a polynomial's zeros under an additive perturbation of the coefficients, and we apply the metric to optimize the J-BMOCZ zero constellation parameters. We then combine the advantages of J-BMOCZ and Huffman BMOCZ to design a hybrid waveform for OFDM with BMOCZ (OFDM-BMOCZ). The pilot-free waveform enables blind synchronization/detection and has a fixed peak-to-average power ratio that is independent of the message. Finally, we assess the proposed scheme through simulation and demonstrate non-coherent OFDM-BMOCZ using low-cost software-defined radios.