Fully convolutional networks have become the backbone of modern medical imaging due to their ability to learn multi-scale representations and perform end-to-end inference. Yet their potential for slice-to-volume reconstruction (SVR), the task of jointly estimating 3D anatomy and slice poses from misaligned 2D acquisitions, remains underexplored. We introduce a fast convolutional framework that fuses multiple orthogonal 2D slice stacks to recover coherent 3D structure and refines slice alignment through lightweight model-based optimization. Applied to fetal brain MRI, our approach reconstructs high-quality 3D volumes in under 10s, with 1s slice registration and accuracy on par with state-of-the-art iterative SVR pipelines, offering more than speedup. The framework uses non-rigid displacement fields to represent transformations, generalizing to other SVR problems like fetal body and placental MRI. Additionally, the fast inference time paves the way for real-time, scanner-side volumetric feedback during MRI acquisition.