The 3~GeV Rapid-Cycling Synchrotron (RCS) at J-PARC supplies a high-intensity beam to the Main Ring synchrotron (MR). Under the present operating conditions, the RCS extraction bunch is intentionally injected into the MR RF bucket in a mismatched condition. This mismatch causes the bunch to dilute within the MR bucket, which rapidly increases the bunching factor $B_f$, defined as the ratio of average to peak current, and raises it to the desired value immediately after injection. Increasing the bunching factor $B_f$ is essential for reducing beam losses caused by space-charge effects. Although this scheme has been effective for improving $B_f$, the dilution process also produces oscillations in the bunch profile and leads to local reductions of $B_f$, which contribute to beam losses immediately after MR injection. To achieve higher beam power in future MR operation, it is therefore desirable to increase $B_f$ before injection into MR, so that beam losses at the beginning of acceleration can be suppressed. A method called "bunch lengthening" has been proposed to stretch the RCS extraction beam bunch. This method stretches the bunch and increases the $B_f$. It is based on driving a second harmonic RF voltage in the latter part of acceleration and placing the beam at the unstable fixed point (UFP). Experiments on bunch lengthening with low-intensity beams, conducted in RCS and MR, demonstrated the stretching of the RCS extraction beam. The $B_f$ increased from approximately 0.2 to 0.4 in both simulations and beam experiments. These results indicate that the longitudinal beam matching between RCS and MR has improved. To further optimize bunch lengthening, the deformation process of the stretched bunch was investigated. The second harmonic RF voltage was applied twice with optimized timing, resulting in improved longitudinal matching. A detailed presentation of the bunch lengthening and the results of demonstration tests conducted on the J-PARC synchrotrons is provided. The examination results on the optimization of bunch lengthening are also reported.