In this paper, we tackle the complexity of coexisting disorder and Coulomb electron-electron interactions (CEEIs) in solids by addressing a strongly disordered system with intricate CEEIs and a screening that changes both with charge carrier doping level Q and temperature T. We report on an experimental comparative study of the T dependencies of the electrical conductivity σ and magnetic susceptibility χ of polyaniline pellets doped with dodecylbenzenesulfonic acid over a wide range. This material is special within the class of doped polyaniline by exhibiting in the electronic transport a crossover between a low-T variable range hopping (VRH) and a high-T nearest-neighbor hopping (NNH) well below room temperature. Moreover, there is evidence of a soft Coulomb gap ΔC in the disorder band, which implies the existence of a long-range CEEI. Simultaneously, there is an onsite CEEI manifested as a Hubbard gap U and originating in the electronic structure of doped polyaniline, which consists of localized electron states with dynamically varying occupancy. Therefore, our samples represent an Anderson-Mott insulator in which long-range and short-range CEEIs coexist. The main result of the study is the presence of a crossover between low- and high-T regimes not only in σ(T) but also in χ(T), the crossover temperature T∗ being essentially the same for both observables over the entire doping range. The relatively large electron localization length along the polymer chains results in U being small, between 12 and 20 meV for the high and low Q, respectively. Therefore, the thermal energy at T∗ is sufficiently large to lead to an effective closing of the Hubbard gap and the consequent appearance of NNH in the electronic transport within the disorder band. ΔC is considerably larger than U, decreasing from 190 to 30 meV as Q increases, and plays the role of an activation energy in the NNH.