Long duration energy storage devices, such as redox flow batteries (RFBs), are critical for enabling the widespread adoption of renewable energy sources such as wind and solar on the electric grid. Non-aqueous RFBs (NARFBs) have emerged as a possible alternative to aqueous RFBs (e.g., all-vanadium and Zn/Br systems), as they have the potential to use supporting electrolytes with wide operating voltage windows (>3 V) and a variety of redox couples. One NARFB of interest is a hybrid RFB that utilizes an alkali metal anode, such as sodium, and a polysulfide catholyte. However, the realization of a hybrid NARFB for long duration energy storage requires the development of new membranes with robust mechanical properties, good (electro)chemical stability, high ionic conductivity, and low polysulfide permeability. In this work, we have utilized a cation exchange pentablock copolymer membrane with sodium sulfonate and sodium trifluoromethanesulfonimide (TFSI) functionalities. We studied various crosslinking methods with the goal of reducing electrolyte uptake and polysulfide crossover of the membrane, while maintaining high ion transport. One lightly crosslinked membrane exhibits a 40% reduction in electrolyte uptake compared to the uncrosslinked membrane, but at the expense of a reduction in ionic conductivity from 2.5 x 10-4 S/cm to 4.2 x 10-5 S/cm at 20 °C. Our continued efforts in developing techniques to improve membrane properties will also be discussed.