This article presents a novel enhancement to the random spreading based coding scheme developed by Pradhan et al.\ for the unsourced multiple access channel. The original coding scheme features a polar outer code in conjunction with a successive cancellation list decoder (SCLD) and a hard-input soft-output MMSE estimator. In contrast, the proposed scheme employs a soft-input soft-output MMSE estimator for multi-user detection. This is accomplished by replacing the SCLD based polar code with an LDPC code amenable to belief propagation decoding. This novel framework is leveraged to successfully pass pertinent soft information between the MMSE estimator and the outer code. LDPC codes are carefully designed using density evolution techniques to match the iterative process. This enhanced architecture exhibits significant performance improvements and represents the state-of-the-art over a wide range of system parameters.