Bayesian deep Gaussian processes (DGPs) outperform ordinary GPs as surrogate models of complex computer experiments when response surface dynamics are non-stationary, which is especially prevalent in aerospace simulations. Yet DGP surrogates have not been deployed for the canonical downstream task in that setting: reliability analysis through contour location (CL). Level sets separating passable vs. failable operating conditions are best learned through strategic sequential design. There are two limitations to modern CL methodology which hinder DGP integration in this setting. First, derivative-based optimization underlying acquisition functions is thwarted by sampling-based Bayesian (i.e., MCMC) inference, which is essential for DGP posterior integration. Second, canonical acquisition criteria, such as entropy, are famously myopic to the extent that optimization may even be undesirable. Here we tackle both of these limitations at once, proposing a hybrid criteria that explores along the Pareto front of entropy and (predictive) uncertainty, requiring evaluation only at strategically located "triangulation" candidates. We showcase DGP CL performance in several synthetic benchmark exercises and on a real-world RAE-2822 transonic airfoil simulation.