Bosonic modes provide a promising platform for quantum batteries as a result of their unbounded energy spectrum. However, the energy that can be stored during a coherent charging process is limited due to coherent oscillations between the charger and battery. In this work, we show that by introducing a slow quench in the interaction between a coherently driven charger mode and a quadratic oscillator battery, the maximum stored energy and maximum battery power scale algebraically with the quench duration, with exponents controlled by the ramp profile. This finding implies that, quite counterintuitively, slower quenches lead to faster charging. Such a quench suppresses coherent energy oscillations between the battery and the charger, allowing an unbounded increase in power. We further show that, in the ideal closed protocol, the stored energy is fully extractable as ergotropy, while charger dissipation converts the algebraic enhancement into a finite-time scaling window with an optimal quench duration. We also show that the temporal-extensive scaling occurs in a broader context by mapping the system to a coherently driven Tavis-Cummings battery. Finally, we discuss experimentally accessible signatures in superconducting circuit quantum electrodynamics and organic microcavity platforms.