Recent experiments focused on the hypersonic boundary layer transition process have been conducted at JAXA's free-piston shock tunnel HIEST facility. Specifically, the disturbance frequencies associated with the transition process were measured experimentally. In this paper, CFD simulations of the experiments are used to generate mean flow solutions for use in boundary layer stability analyses. The disturbances in the boundary layer are calculated using the linear PSE method. Comparisons of transition location, disturbance amplification rates, and disturbance frequencies are made between those measured experimentally and those calculated from the PSE analysis. Additionally, an investigation of the effects of finite-rate chemistry and vibrational excitation on flows over cones was conducted for theoretical operational conditions at the HIEST facility and for similar experiments previously performed at the GALCIT T5 facility.