The Soft X-ray Spectrometer (SXS) is the first space-based instrument to implement redundancy in the operation of a sub-Kelvin refrigerator. The SXS cryogenic system consists of a superfluid helium tank and a combination of Stirling and Joule-Thompson (JT) cryocoolers that support the operation of a 3-stage adiabatic demagnetization refrigerator (ADR). When liquid helium is present, the x-ray microcalorimeter detectors are cooled to their 50 mK operating temperature by two ADR stages, which reject their heat directly to the liquid at ~1.1 K. When the helium is depleted, all three ADR stages are used to accomplish detector cooling while rejecting heat to the JT cooler operating at 4.5 K. Compared to the simpler helium mode operation, the cryogen-free mode achieves the same instrument performance by controlling the active cooling devices within the cooling system differently. These include the three ADR stages and four active heat switches, provided by NASA, and five cryocoolers, provided by JAXA. Development and verification details of this capability are presented within this paper and offer valuable insights into the challenges, successes, and lessons that can benefit other missions, particularly those employing cryogen-free cooling systems.