NASA and other space agencies have been planning the construction of a space station in lunar orbit called the Gateway. They have also begun studies for its resupply missions using an HTV-X. There are several ways to transition to NRHO, a candidate orbit. In-Direct Transfer (IDT) has a short transition period of seven days, but the required ΔV is inefficient at more than 400 m/s. The Weak Stability Boundary (WSB) transfer requires a small ΔV, less than 100 m/s, but the transition period is more than 100 days. This paper proposes the Perilune Rendezvous Method (PRM), recently discovered in 2022. Its transition period is two weeks longer than IDT, but the period is much shorter than WSB. The required ΔV is 40 m/s lower than IDT but still larger than WSB. The PRM has an intermediate ΔV and a transition period between IDT and WSB. Since fuel consumption and transition duration requirements depend on the mission, the PRM expands the scope of future cargo transportation. To adopt the PRM in a mission, an efficient trajectory correction plan was found based on a Monte Carlo analysis that considered navigation and control errors. It confirmed that the PRM could rendezvous with Gateway with higher accuracy than IDT.