Invertible logic using a probabilistic magnetoresistive device model has been recently presented that can operate in bidirectional ways and solve several problems quickly, such as factorization and combinational optimization. In this paper, we present a design framework for large-scale invertible logic circuits. Our approach makes use of linear programming to create a Hamiltonian library with the minimum number of nodes. In addition, as the device model is approximated based on stochastic computing in SystemVerilog, a faster simulation using the compiled SystemC binary is realized than a conventional SPICE-level simulation. We have evaluated our framework on designing invertible multipliers, which realizes almost 5 order-of-magnitude faster simulation than a conventional method.