We systematically compare seven transformations of the dimensionless tidal deformability Λ against neutron star compactness C = GM/Rc², using 15 nuclear equations of state spanning the full observationally plausible stiffness range and 76 stellar configurations (M ~ 1.0–2.0 M☉).The logarithmic transformation ln(Λ) achieves the highest global linear correlation with C (R² = 0.8296 vs Λ^(1/5): R² = 0.7611). A continuous exponent scan over α ∈ [2, 20] shows R² increasing monotonically — confirming convergence to the logarithmic limit as α → ∞, not the existence of a privileged power-law exponent.A pre-registered per-EoS residual test — the decisive methodological contribution of this work — shows that ln(Λ) reduces per-EoS scatter in only 1 of 15 EoS families. The global R² advantage is therefore primarily statistical, arising from heavy-tail compression of the Λ distribution, not from improved physical universality. This null result is reported and incorporated into the analysis, redirecting focus toward the α(C) direction.The effective local exponent n = d ln(Λ)/d ln(C) varies from −3.52 to −2.26 (mean −2.99 ± 0.33) across EoS — a systematic departure from the theoretical value −5. A cross-validation against Zhao & Lattimer (2018) shows that our linear ln(Λ)–C model achieves competitive accuracy relative to their quadratic fit despite using fewer parameters, independently confirming ln(Λ) as the natural coordinate for this class of relations.The most promising direction identified is a compactness-dependent effective exponent α(C). If demonstrated to be partially EoS-independent on a larger sample, it could constitute a new phenomenological relation complementary to the I-Love-Q framework. All results are consistent with General Relativity and with Yagi & Yunes (2013).This work is purely exploratory and phenomenological in character. Version 4 includes: systematic exponent scan with convergence analysis; pre-registered per-EoS decisive test; cross-validation against Zhao & Lattimer (2018); quantitative comparison with the I-Love-Q framework; honest null-result reporting; updated figures and statistical diagnostics.Dataset: 15 nuclear equations of state, 76 stellar configurations. Values compiled from literature: Read et al. (2009), Hinderer et al. (2010), Abbott et al. (2018), and NICER observational constraints (Riley et al. 2019, 2021; Miller et al. 2019, 2021; Choudhury et al. 2024).