End-to-end (E2E) designed imaging systems integrate coded optical designs with decoding algorithms to enhance imaging fidelity for diverse visual tasks. However, existing E2E designs encounter significant challenges in maintaining high image fidelity at wide fields of view, due to high computational complexity, as well as difficulties in modeling off-axis wave propagation while accounting for off-axis aberrations. In particular, the common approach of placing the encoding element into the aperture or pupil plane results in only a global control of the wavefront. To overcome these limitations, this work explores an additional design choice by positioning a DOE off-aperture, enabling a spatial unmixing of the degrees of freedom and providing local control over the wavefront over the image plane. Our approach further leverages hybrid refractive-diffractive optical systems by linking differentiable ray and wave optics modeling, thereby optimizing depth imaging quality and demonstrating system versatility. Experimental results reveal that the off-aperture DOE enhances the imaging quality by over 5 dB in PSNR at a FoV of approximately $45^\circ$ when paired with a simple thin lens, outperforming traditional on-aperture systems. Furthermore, we successfully recover color and depth information at nearly $28^\circ$ FoV using off-aperture DOE configurations with compound optics. Physical prototypes for both applications validate the effectiveness and versatility of the proposed method.