The F10.7 solar radio flux is a critical quantity for operational space weather nowcasting and forecasting, where it is routinely used as a driver for coupled atmospheric models to estimate a variety of important quantities such as the neutral atmospheric density. Although there have been several successful developments in the way of parametric modeling to ensure F10.7 coverage during outages (often using the sunspot number or radio flux observations at neighboring wavelengths), these developments refrained from employing comprehensive cross-validation schemes to ensure model generalizability, and can stand to benefit from recently-developed techniques for modeling nonlinear phenomena. We present an approach that uses Feature Ordering by Conditional Independence (FOCI) to identify favorable surrogates for the F10.7 index through a series of distance computations, and combines this with modeling of F10.7 with linear models and Generalized Additive Models (GAM). We find that this approach offers notable improvements in reconstructing F10.7 over gaps of various lengths, with GAMs yielding mean error of ∼2.7%, compared to polynomial methods that yield mean errors of ∼3.1%. We additionally demonstrate the effect of reconstruction error on neutral densities modeled by the NRLMSISE2.0 thermosphere model.