We report measurements of the viscoelastic parameters associated with the twist distortion of polymer-stabilized liquid crystal materials (PSLC), made by polymerizing 4,4′-bis-(acryloyloxy)-1,1′-biphenylene (BAB) and 4-butoxybenzyl 4-[6-(methacryloyloxyl-hexyloxy]benzoate (BMB6) to form fibrous networks in a nematic liquid crystal solvent (4′-phenyl-4-cyanobiphenyl, 5CB). By varying the BAB/BMB6 ratio, the twist elastic constant, K22, and viscosity, γ1, were investigated over a range of crosslink densities using electric-field-dependent dynamic light scattering (EFDLS). In PSLC samples, the formation of a highly-crosslinked, phase-separated polymer network can lead to optically heterogeneous behavior of the EFDLS data. Thus, it is necessary to evaluate the ensemble-averaged EFDLS relaxation function through spatial averaging. The results show that the polymer network causes a change in the twist relaxation rate, depending on the cross-link density of the specimens. The twist viscosity was found to increase with decrease in cross-link density, which appears to occur because higher cross-link density causes collapse of the gel fibers and less interaction between the fibers and nematic medium.