Amorphous alkali oxychlorides are fast ion conductors, but their atomic structure remains unresolved. Total scattering sums all partial pair correlations into one curve that has no unique inversion, so the structure must be modeled. Melt-quench molecular dynamics builds a model from the interatomic potential alone, and reverse Monte Carlo (RMC) builds one from the measurement alone. The two have rarely been compared with all else held fixed. We benchmark both routes and two hybrid schemes on amorphous ceLi₀.9NbO₀.9Cl₄.1 against one neutron pair distribution function with one foundation potential. The hybrid schemes put the energy either in the acceptance rule (inline) or in short relaxations between blocks of refinement (alternating). Each refinement starts from a melt-quench glass or from a random packing of isolated units. The glass has the lowest energy and places the first-shell peaks correctly, but carries almost none of the oscillation beyond 6 Å (goodness of fit R² = 0.29). Pure RMC fits the measurement to within its counting noise (R² = 0.99), but at more than 1.3~eV/atom above the glass, and niobium loses about half of its first-shell chlorine. Started from the glass, both hybrid schemes reach R² = 0.92 within 0.1~eV/atom of its energy and keep its coordination chemistry. Structures from the two inputs fit almost equally well and differ in energy by a tenth of the RMC penalty, yet they differ in whether their polyhedra are connected. The input is therefore part of the method. We recommend quenching a glass with a foundation potential and refining it against the measurement with a hybrid scheme. The resulting structure carries both the local chemistry and the medium-range order, and it is the starting point for modeling ion transport in these conductors.