Dynamic Spectrum Access (DSA) is a key mechanism for meeting the ever-increasing demand for emerging wireless services. DSA involves managing and assigning available spectrum resources in a way that minimizes interference and allows RF coexistence between heterogeneous devices and systems. Spectrum Consumption Models (SCMs)-defined in the IEEE 1900.5.2 standard, offer a mechanism for RF devices to: (i) declare the characteristics of their intended spectrum use and their interference protection needs; and (ii) determine compatibility (non-interference) with existing devices. In this paper, we propose a novel SCM-based Spectrum Deconfliction (SD) algorithm that dynamically configures RF operational parameters (e.g., center frequency and transmission power) of a target transmitter-receiver pair aiming to minimize interference with existing devices/systems. We also propose sequential and distributed DSA methods that use the SD algorithm for assigning spectrum in large-scale networks. To evaluate the performance of our methods in terms of computation time, spectrum assignment efficiency, and overhead, we use two custom-made simulation platforms. Finally, to experimentally demonstrate the feasibility of our methods, we build a proof-of-concept implementation in the NSF PAWR COSMOS wireless testbed. The results reveal the advantages of using SCMs and their capabilities to conduct spectrum assignments in dynamic and congested communication environments.