The inter-regional electricity market is instrumental in enhancing the economic efficiency, reliability, and integration of renewable generation within interconnected power systems. As the market boundary expands, the complexity and solution difficulties of market clearing increase rapidly. The presence of hybrid alternating current (AC)/direct current (DC) interconnector networks further compounds challenges in modeling trading paths and transmission tariffs. To address these issues, this paper proposes a path-aware market-clearing (PAMC) model tailored for the inter-regional electricity market, which accommodates the hybrid AC/DC interconnector network. A variable aggregation strategy is proposed to reduce the problem scale while ensuring equivalent optimality. In addition, a novel redundancy elimination method is developed to expedite the solution of the market-clearing problem. This framework utilizes envelope approximations of residual demand curves to identify bidding blocks that will not affect the marginal price. Corresponding decision variables are then constrained to their bounds to remove redundant information. Comprehensive case studies across different power system scales validate the superiority of the proposed PAMC model in improving social welfare, and verify the effectiveness of the proposed redundancy elimination method in accelerating the solution of the market-clearing problem.