Computational thinking (CT) is a critical thinking skill and an essential component of digital competence frameworks for problem-solving. Kosovo's education system represents an emerging context where digital integration and CT initiatives are underway yet face systemic implementation challenges. This study examined Kosovo teachers' perceptions of CT integration and identified strategic intervention points using the leverage points framework from systems thinking. Through mixed-methods analysis of survey data and focus group discussions with teachers, current and ideal CT integration were mapped across leverage point levels. Findings revealed moderate CT knowledge among teachers and positive attitudes toward its cross-curricular integration, yet they faced barriers including content-heavy curricula, rigid assessment structures, and inadequate professional development. Systemically, an intervention hierarchy was modeled with different effectiveness levels, ranging from low-leverage areas such as class size and infrastructure to high-leverage areas such as shifting the system's goal toward competency-based education. This teacher-informed typology provides a practical diagnostic tool for digital education reform in similar contexts. The study offers three key implications. Theoretically, the study operationalizes the leverage points framework through empirical data. Practically, findings prioritize competency-focused assessment and teacher autonomy. For policy, the framework recommends cross-disciplinary CT curricula with structural reforms fostering teacher self-organization in resource-constrained contexts.