Systematic discovery of optimization paths in quantum circuit simplification remains a challenge. Today, ZX-calculus, a computing model for quantum circuit transformation, is attracting attention for its highly abstract graph-based approach. Whereas existing tools such as PyZX and Quantomatic offer domain-specific support for quantum circuit optimization, visualization and theorem-proving, we present a complementary approach using LMNtal, a general-purpose hierarchical graph rewriting language, to establish a diagrammatic transformation and verification platform with model checking. Our methodology shows three advantages: (1) a direct and concise encoding of the ZX-calculus, where quantifiers simplify complex rule specification; (2) a verification framework using state-space exploration and model checking to analyze rewrite strategies; and (3) an open platform for strategic experimentation combining programmable syntax with interactive visualization. Through case studies, we demonstrate how our framework helps understand optimization paths and design new algorithms and strategies. This suggests that the declarative language LMNtal and its toolchain could serve as a new platform to investigate quantum circuit transformation from a different perspective.