In the Multi-Agent Pathfinding with Matching (MAPFM) problem, agents from a team are matched with and routed towards one of their team's goals without colliding with other agents. The sum of path costs of all agents is minimized. In prior works, Conflict Based Min-Cost-Flow (CBM) has been proposed. This algorithm solves a similar problem that instead minimizes the maximum path length. In this paper, an extension upon CBM is presented, called CBMxSOC. It consists of several changes to CBM that allow it to minimize the sum of path costs. CBMxSOC is experimentally compared to other MAPFM solvers and is shown to be able to scale to many agents when there are few conflicts between different teams.