When multiple weight matrices are encoded in a shared wave-optical volume, adding matrices can improve rather than degrade per-matrix fidelity — an effect we term cooperative encoding. A companion paper observed this phenomenon in Cartesian angle-multiplexed volumes but could not explain it or study it at scale, because cross-talk between angular channels imposes a hard capacity cliff near N ≈ 12. This paper identifies the mechanism and provides the geometric tools to study it at scale. Reformulating the Beam Propagation Method (BPM) in cylindrical coordinates replaces the approximate Bragg selectivity of the Cartesian system with structurally exact Fourier-mode orthogonality in the addressing scheme, removing the channel cliff. Generalising to K rotational axes — a simulation-native mathematical extension with no physical counterpart for K ≥ 2 — provides exponential channel addressing (s^(K−1) channels for s modes per axis). We demonstrate 64 32×32 matrices coexisting in a single four-rotation volume at 0.010 MAE with uniform per-channel fidelity (a representative single run; per-channel distribution in Section 5.3 and the supplementary material). At K = 2, where a single matrix encodes poorly (0.554 MAE) because the volume is under-constrained, adding matrices improves worst-case precision 7× across the clean range (N = 1 to N = 50); within each readout regime the same qualitative improvement appears at higher K, compressed as the better-conditioned starting point leaves less room for it (we compare curve shape across K, not absolute MAE, since the readout differs — Section 4.4). Mechanism experiments at K = 1 are consistent with cooperation arising from constraint diversity in an overparameterised inverse problem: orthogonal targets achieve up to ~6× lower MAE than random targets, per-channel gradients become approximately orthogonal as N grows, and adding helper channels to a converged solo encoding actively improves its precision. These mechanism results are measured at K = 1; at K ≥ 3 we observe the same qualitative improvement with N but do not claim the gradient-level correlates transfer quantitatively. A modal Fourier readout — projection onto the addressing basis rather than spatial sampling — is required at K ≥ 3, where a spatial slice discards 1/∏ⱼ N_θⱼ of the signal energy. The precision floor of ~0.01 MAE appears to be solver-limited rather than capacity- or dimensionality-limited.