Unmanned aerial vehicle (UAV) corridor-assisted communication networks are expected to expand significantly in the upcoming years driven by several technological, regulatory, and societal trends. In this new type of networks, accurate and realistic channel models are essential for designing reliable, efficient, and secure communication systems. In this paper, an analytical framework is presented that is based on one-dimensional (1D) finite point processes, namely the binomial point process (BPP) and the finite homogeneous Poisson point process (HPPP), to model the spatial locations of UAV-Base Stations (UAV-BSs). To this end, the shadowing conditions experienced in the UAV-BS-to-ground users links are accurately considered in a realistic maximum power-based user association policy. Subsequently, coverage probability analysis under the two spatial models is conducted, and exact-form expressions are derived. In an attempt to reduce the analytical complexity of the derived expressions, a dominant interferer-based approach is also investigated. Finally, the main outcomes of this paper are extensively validated by empirical data collected in an air-to-ground measurement campaign. To the best of the authors' knowledge, this is the first work to experimentally verify a generic spatial model by jointly considering the random spatial and shadowing characteristics of a UAV-assisted air-to-ground network.