Shock tube experiments provide critical insight into the thermochemical processes that occur in the shock layer of hypersonic flight vehicles and are used to validate many chemical-kinetic and radiative models for vehicle design. Shock tube flows exhibit a number of non-ideal behaviours that must be accounted for when interpreting experimental data. Previous work has shown that variations in shock speed and boundary layer growth along the length of the shock tube have a strong effect on the test slug properties. The LAgrangian Shock Tube Analysis code (LASTA) is an a posteriori tool that successfully addressed this problem, allowing reconstruction of the test slug from an experimentally obtained shock trajectory. LASTA 2.0 is presented here, which further constrains the test slug properties using an additional experimental pressure boundary condition whose effects are included via a backwards time integration scheme. The tool is validated against ideal gas cases following accelerating and decelerating shock trajectories, each with a tube-end Mach number of 6.5 and a fill pressure of 66.66 Pa. Agreement between the method and results from a viscous, axisymmetric Navier-Stokes solution is found to be within 1% in pressure and temperature in the majority of cases. Improved agreement with experimental data is evident when compared to the previous version of LASTA, particularly where there is strong shock speed non-uniformity.