Deploying Automatic Speech Recognition (ASR) models on memory-constrained edge devices requires aggressive low-bit weight quantization. Layer-wise post-training quantization is practical and effective, but it suffers from cross-layer error accumulation. Existing compensation methods typically use a single global strength for all layers, which is ill-suited to encoder-decoder ASR models whose acoustic encoder and linguistic decoder exhibit markedly different sensitivities to quantization noise. We propose FADE, a diagnostic-driven framework that assigns each layer an adaptive compensation coefficient by combining two complementary signals: an intrinsic vulnerability score from weight geometry and a calibration reliability score from the data-driven solution. The resulting layer-wise coefficient balances local quantization fidelity against cross-layer error correction, enabling tailored compensation without retraining or hyperparameter search. Experiments on Whisper, Moonshine, and Qwen3-ASR across four benchmarks show that FADE consistently improves mean Word Error Rate over strong baselines at both 3- and 4-bit precision while substantially reducing run-to-run variance.