High-dynamic-range (HDR) imaging is an essential technique for overcoming the dynamic range limits of image sensors. The classic method relies on multiple exposures, which slows capture time, resulting in motion artifacts when imaging dynamic scenes. Single-shot HDR imaging alleviates this issue by encoding HDR data into a single exposure, then computationally recovering it. Many established methods use strong image priors to recover improperly exposed image detail. These approaches struggle with extended highlight regions. We utilize the global reset release (GRR) shutter mode of an off-the-shelf sensor. GRR shutter mode applies a longer exposure time to rows closer to the bottom of the sensor. We use optics that relay a randomly permuted (shuffled) image onto the sensor, effectively creating spatially randomized exposures across the scene. The exposure diversity allows us to recover HDR data by solving an optimization problem with a simple total variation image prior. In simulation, we demonstrate that our method outperforms other single-shot methods when many sensor pixels are saturated (10% or more), and is competitive at a modest saturation (1%). Finally, we demonstrate a physical lab prototype that uses an off-the-shelf random fiber bundle for the optical shuffling. The fiber bundle is coupled to a low-cost commercial sensor operating in GRR shutter mode. Our prototype achieves a dynamic range of up to 73dB using an 8-bit sensor with 48dB dynamic range.