Laser Speckle Rheology (LSR) is an optical technique to evaluate the viscoelastic properties by analyzing the temporal fluctuations of backscattered speckle patterns. Variations of optical absorption and reduced scattering coefficients further modulate speckle fluctuations, posing a critical challenge for quantitative evaluation of viscoelasticity. We compare and contrast two different approaches applicable for correcting and isolating the collective influence of absorption and scattering, to accurately measure mechanical properties. Our results indicate that the numerical approach of Monte-Carlo ray tracing (MCRT) reliably compensates for any arbitrary optical variations. When scattering dominates absorption, yet absorption is non-negligible, diffusing wave spectroscopy (DWS) formalisms perform similar to MCRT, superseding other analytical compensation approaches such as Telegrapher equation. The computational convenience of DWS greatly simplifies the extraction of viscoelastic properties from LSR measurements in a number of chemical, industrial, and biomedical applications.