Squeezing of the collective spin of an ensemble of atoms is intimately related to the creation of entanglement and nonlinear evolution of the many-body system. We describe a new approach to achieving a high degree of squeezing based on coherent quantum feedback in a double-pass Faraday interaction between an optical probe and an optically dense atomic sample. A quantum eraser is used to remove residual spin-probe entanglement, thereby realizing a single-axis twisting unitary map on the collective spin. This interaction can be phase-matched, resulting in *exponential* enhancement of squeezing as a function of optical density for times short compared to the decoherence time. In practice the scaling and peak squeezing depends on decoherence, technical loss, and noise. Including these imperfections, our model indicates that 10 dB of squeezing should be achievable with laboratory parameters. With such squeezing as a base, we can explore the atomic ensemble as a platform for continuous-variable quantum information processing.