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The management of RF spectrum resources between heterogeneous RF devices has become more challenging with the advent of 5G, 6G and the desire to enable more spectrum sharing interactions in different bands. Most of the research on Dynamic Spectrum Access (DSA) algorithms considers non-cooperative scenarios with RF devices using omnidirectional antennas. In this paper, we study the effects of antenna directionality on cooperative DSA. Specifically, we develop a custom simulator for large-scale DSA networks that leverages IEEE 1900.5.2 Spectrum Consumption Models (SCMs) to enable coordination and computation of aggregate interference to deconflict spectrum use in large scale scenarios. SCMs offer a mechanism for RF devices to describe the characteristics of their use of spectrum and their needs in terms of interference protection. We create SCMs for RF systems with directional antennas based on measurements from a directional mmWave antenna and from the operational characteristics defined by the European Telecommunications Standards Institute (ETSI). We leverage these SCMs to perform a comparative analysis of spectrum use efficiency in cooperative DSA networks with up-to 300 links of transmitter-receiver RF devices using omnidirectional antennas vs similar networks using directional antennas with different half-power beam widths. The simulation results show the benefits to spectrum use efficiency that can be achieved with directional antennas and how largescale DSA methods can be studied and designed with the use of SCMs that incorporate detailed characteristics of directional antennas.