To effectively keep pace with the global IP traffic growth forecasted in the years to come, flex-grid over multi-core fiber (MCF) networks can bring superior spectrum utilization flexibility, as well as bandwidth scalability far beyond the non-linear Shannon's limit. In such a network scenario, however, full node switching re-configurability will require enormous node complexity, pushing the limits of current optical device technologies with prohibitive capital expenditures. Therefore, cost-effective node solutions will most probably be the key enablers of flex-grid/MCF networks, at least in the short- and mid-term future. In this context, this paper proposes a cost-effective reconfigurable optical add/drop multiplexer (ROADM) architecture for flex-grid/MCF networks, called CCC-ROADM, which reduces technological requirements (and associated costs) in exchange for demanding core continuity along the end-to-end communication. To assess the performance of the proposed CCC-ROADM in comparison with a fully flexible ROADM (i.e., a fully non-blocking ROADM, called FNB-ROADM in this work) in large-scale network scenarios, a novel lightweight heuristic to solve the route, modulation, core, and spectrum assignment problem in flex-grid/MCF networks is presented in this work, whose goodness is successfully validated against optimal ILP formulations previously proposed for the same goal. The obtained numerical results in a significant number of representative network topologies with different MCF configurations of 7, 12, and 19 cores show almost identical network performance in terms of maximum network throughput when deploying CCC-ROADMs versus FNB-ROADMs, while decreasing network capital expenditures to a large extent.