Reliability estimation for early-stage aircraft design workflows is challenging because multidisciplinary simulations are computationally expensive, failures of probabilistic requirements are rare, and uncertainties are substantial. In practice, engineers typically select a single reliability method: such as First-Order Reliability Methods (FORM) or sampling-based approaches like Importance Sampling (IS) and Subset Simulation (SubSim) based largely on experience, switching methods only after excessive computational cost or non-convergence is observed. Although surrogate-based reliability methods can reduce model evaluations, their effectiveness depends strongly on problem characteristics such as smoothness and failure-boundary complexity, limiting reproducibility at the workflow level. This work proposes a budget-aware reliability controller that formulates method selection as a progressive, diagnostic-driven decision process. The controller begins with low-cost diagnostics, including failure-rarity screening, effective-dimension screening, and failure-geometry probing using FORM as a diagnostic tool to assess design-point stability and indications of single versus multi-region failure structures. Based on these diagnostics, the controller automatically selects and orchestrates reliability methods, favoring IS for stable single-region failures, SubSim for complex or uncertain failure geometries, and surrogate-assisted reliability when computational cost dominates. The framework is validated on representative reliability benchmarks and further applied to an aircraft-relevant requirement verification workflow to enable reproducible and cost-aware reliability analysis for expensive multidisciplinary design workflows.