Recent theory proposes that edge dislocations in random body-centered cubic (BCC) high entropy alloys have high barriers for motion, conveying high strengths up to high temperatures. Here, the energy barriers for edge motion are computed for two model alloys, NbTaV and MoNbTaW as represented by interatomic potentials, using the Nudged Elastic Band method and compared to theoretical predictions. The average magnitude of the barriers and the average spacing of the barriers along the glide direction agree well with the analytical theory, with no adjustable parameters. The evolution of the barriers versus applied stress is modeled, and the mean strength is in reasonable agreement with the predicted zero-temperature strength. These findings validate the analytic theory. A reduced analytic model based on solute misfit volumes is then applied to Hf-Mo-Nb-Ta-Ti-Zr and Mo-Nb-Ta-Ti-V-W alloys, rationalizing the observed significant strength increases at room temperature and 1000 C-circle upon addition of solutes with large misfit into a base alloy. The analytic theory for edge motion is thus a powerful validated tool for guiding alloy selection.