We present a structural pharmacology framework for cancer drug discovery based on perturbation analysis of multi-layer signaling networks. Across six cancer types (KRAS-NSCLC, CRC, PDAC, GBM, BRAF-melanoma, EGFR-NSCLC), we compute the delta-r of each signaling protein — the change in inter-layer Pearson correlation upon node removal — and classify proteins as structural dampers (delta-r > 0) or anchors (delta-r < 0). Two pre-registered null model tests reveal that raw delta-r contains a strong degree-dependent component. We remove it via z_δr(v) = [δr(v) − μ_null(v)] / σ_null(v), yielding a degree-corrected structural perturbation metric (z_δr). A pre-registered degree-independence test (DISC_CANCER_7, 4/4 confirmed) validates this: global Spearman r(degree rank, |z_δr| rank) = 0.24 across 94 protein-network pairs. Key findings: CDK4 emerges as a robust degree-corrected structural damper in PDAC (|z_δr| > 2.0 under both null types) despite ranking 10th of 16 by degree. SOS1 is the top structural damper in EGFR-mutant NSCLC (z_δr = +2.47, rank 12th of 15 by degree), identifying it as a high-priority structural target not highlighted by degree centrality. MEK1 switches regime across cancer types (damper in ODS cancers, anchor in BRAF-melanoma), a signal invisible to degree centrality and pharmacologically validated: MEK inhibitors show the largest dissociation vs. GBM (d = −0.62, p < 10⁻¹⁰) and vs. CRC (d = −0.19, p < 10⁻¹⁰). DAMPER-Essentiality Decoupling: structural damper status predicts pharmacological vulnerability but not CRISPR essentiality. SOS1 (top damper in KRAS-MT LUAD, z_δr = +4.184) is not CRISPR-essential (d = +0.522, p = 0.29), while KRAS is (d = −1.336, p = 0.0002). Replicated in EGFR-MT LUAD (D23). Boundary conditions: z_δr predictions hold for co-pathway targets but fail for indirect activation (STAT3 via EGFR in GBM, p = 0.55) and state-dependent accessibility (MDM2 in PDAC, where ~70% TP53 mutation rate overrides structural signal). Reproducibility: Most validation experiments were pre-registered before data access. Analysis scripts, preregistrations, and dataset acquisition instructions are provided in the repository and paper.