Let $V$ be a valuation ring with fraction field $K$, let $L=K(\alpha)$ be a finite simple extension, and let $A=V[\alpha]\subseteq W$, where $W$ denotes the integral closure of $A$ in $L$. We study homological defect modules associated to the normalization quotient $W/A$ using ordinary derived functors. For every valuation-compatible ideal $I\subseteq A$, we define derived integral closure defects \[ \operatorname{Tor}_i^A(W/A,A/I), \] which measure the failure of reduction modulo $I$ to preserve exactness of the normalization sequence \[ 0\to A\to W\to W/A\to0. \] The new content is the systematic valuation-theoretic use of these ordinary Tor groups as normalization-defect invariants: we identify their conductor support, isolate the connecting image as the actual obstruction to exact reduction, and compute their \(\pi\)-primary torsion profiles in DVR-order normalizations. In particular, in the DVR-order setting the first derived defect records the \(\pi\)-primary normalization-quotient thickness, including non-cyclic elementary-divisor profiles. In ramified DVR-order examples this profile may reflect ramified structure, but the Tor computation itself is an invariant of the normalization quotient rather than a ramification invariant. The approach is entirely algebraic and valuation-theoretic, using only classical homological methods and avoiding higher-categorical or spectral machinery.