Although the MeV gamma-ray band is a promising energy-band window in astrophysics, the current situation of MeV gamma-ray astronomy significantly lags behind those of the other energy bands in angular resolution and sensitivity. An electron-tracking Compton camera (ETCC), a next-generation MeV detector, is expected to revolutionize the situation. An ETCC tracks each Compton-recoil electron with a gaseous electron tracker and determines the incoming direction of each gamma-ray photon; thus, it has a strong background rejection power and yields a better angular resolution than classical Compton cameras. Here, we study ETCC events in which the Compton-recoil electrons do not deposit all energies to the electron tracker but escape and hit the surrounding pixel scintillator array (PSA). The PSA provides additional information on the electron-recoil direction, which enables us to improve significantly the angular resolution. We developed an analysis method for this untapped class of events and applied it to laboratory and simulation data. We found that the energy spectrum obtained from the simulation agreed with that of the actual data within a factor of 1.2. We then evaluated the detector performance using the simulation data. The angular resolution for the new-class events was found to be twice as good as in the previous study at the energy range 1.0–2.0 MeV, where both analyses overlap. We also found that the total effective area is dominated by the contribution of the double-hit events above an energy of 1.5 MeV. Notably, applying this new method extends the sensitive energy range with the ETCC from 0.2–2.1 MeV in the previous studies to up to 3.5 MeV. Adjusting the PSA dynamic range should improve the sensitivity in even higher energy gamma-rays. The development of this new analysis method would pave the way for future observations by ETCC to fill the MeV-band sensitivity gap in astronomy.