Many desirable material properties may be associated with disorder exhibiting local periodicity or correlations. However, few systems allow systematic studies into the effects of intrinsic crystallographic conflict on correlated disorder. The authors use epitaxial matching to stabilize an exemplar system: the pseudo-bcc U${}_{1\ensuremath{-}x}$Mo${}_{x}$ alloy, which exhibits a significant mismatch between the basis preferred symmetry and the global lattice. Employing diffuse and inelastic x-ray scattering techniques on 300-nm epitaxial films, combined with $a\phantom{\rule{0}{0ex}}b$ $i\phantom{\rule{0}{0ex}}n\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}o$ modeling, the authors discover a new form of correlated disorder which exhibits strong disorder-phonon coupling that dramatically suppresses phonon lifetimes. These findings have implications across a broad range of materials and could be exploited to develop future functional materials.