Spin-orbit interaction of light in a disordered anisotropic medium is known to yield spin split modes in the momentum domain because of the random spatial gradient of the geometric phase of light. Here, we have studied the statistics of such spin-split modes for beams carrying intrinsic orbital angular momentum through the quantification of momentum domain entropy and investigated its dependence on various beam parameters. The influence of the spatial structure of the beam and the phase vortex on the statistics of the spin split modes were separately investigated using input Laguerre-Gaussian and Perfect Vortex beams passing through a disordered anisotropic medium with controlled input disorder parameter, which was realized by modulating the pixels of a liquid crystal-based spatial light modulator. The results of systematic investigations on the impact of beam waist, spot size and topological charge of the vortex beam show that the influence of the spot size on the emergence of the random spin split modes is much more significant as compared to the other beam parameters.