While machine-learned interatomic potentials (MLIPs) accelerate phonon dispersion calculations, merely identifying dynamical instabilities in computationally predicted materials is insufficient; automated pathways to resolve them are required. We introduce VibroML, an open-source Python toolkit driven by foundational MLIPs that shifts the paradigm from stability verification to automated structural remediation. VibroML employs an energy-guided genetic algorithm that vastly outperforms traditional soft-mode following, efficiently navigating the potential energy surface to uncover diverse, dynamically stable polymorphs. As 0 K harmonic stability does not guarantee macroscopic viability, an automated molecular dynamics workflow evaluates finite-temperature structural retention. VibroML also couples with ProtoCSP, our combinatorial structure prediction engine, to stabilize frustrated crystal topologies via targeted alloying, successfully rescuing functional perovskite networks like Cs$_2$KInI$_6$ and KTaSe$_3$. Demonstrating broader applicability, we mined the Alexandria database -- where ~50% of quaternary and 99.5% of quinary elemental combinations lack any structural entries -- to identify thousands of abandoned, high-symmetry stoichiometries. Deploying ProtoCSP's "cold start" retrieval and VibroML's evolutionary search on a sample, we successfully identified dynamically stable low-symmetry candidates. Through integrated structural remediation, thermal validation, and systematic compositional exploration, VibroML enables a comprehensive deep-screening approach, yielding physically sound structural propositions that far surpass standard high-throughput workflows.