The DSS most certainly are documents in the North-West Semitic tradition. They did not, however, exist in a vacuum. Nor does the writing system used in these texts stand outside their time frame or as totally divorced from other descendants of the North West-Semitic writing systems.
Writing systems are substantially more than script systems.
All the parts in a system must operate together within the overall system design or the complete system will not work. This rule applies whether we are referring to a plumbing system, an ark, or a writing system. A script system is an important part, but only a part, of a writing system. Each sub-system in a writing system is balanced and designed to work with the others. We must not conflate script systems with writing systems.