We have performed small-angle X-ray scattering (SAXS) measurements to study the evolution of length-scale-dependent nanoparticle (NP) correlations over a wide range of loadings in miscible silica-poly(2-vinylpyridine) polymer nanocomposites (PNC) characterized by strong interfacial attraction. The local cage and intermediate-scale correlations evolve in a commonly observed manner with increasing silica concentration, while long-wavelength concentration fluctuations exhibit a complex behavior. Higher-loading PNCs show a nonmonotonic change in the structure factor amplitude with wavevector because of an upturn on the longest length scales, which is the most intense for the highest NP concentration sample. These observations suggest that the PNC is approaching a spinodal demixing transition of an unusual polymer bridging-induced network type. PRISM integral equation theory is quantitatively applied, captures the key features of the SAXS data, and provides a theoretical basis for a network-like phase separation analogous to polyelectrolyte coacervation. The theory with validated parameters is then used to make predictions of real-space pair correlation functions between all species, the small- and large-wavevector collective polymer structure factor, spatially resolved NP coordination numbers, the interfacial cohesive energy density, and a measure of an enlarged effective NP radius because of polymer adsorption. With increasing NP loading, intensification of tight secondary bridged NP configurations, but weakening of interpolymer and polymer-NP correlations due to packing frustration, is predicted. This local reorganization of the polymer structure coexists with macro- and microphase separation such as features at low wavevectors which vary distinctively with NP loading. The predictions for the collective polymer structure are potentially testable using scattering experiments. Our results provide an important starting point for building an understanding of collective NP dynamics.