by parasitic processes such as drive-induced dephasing and leakage. Here, we demonstrate that sub-GHz charge driving of superconducting Kerr oscillators (KOs) in the transmon regime circumvents this trade-off, simultaneously activating fast parametric interactions and protecting the encoded qubit from low-frequency noise. The key is the frequency dependence of the charge sensitivity: using the AC Stark shift as a probe, we find that the KO frequency sensitivity to a charge drive grows quadratically with both drive frequency and amplitude, making the oscillator weakly sensitive to 1/f charge noise yet strongly coupled to drives near 1~GHz. Exploiting this, we first demonstrate cooling and reset of the KO in 82~ns, to a residual population below 0.7%—lower than its 2.5% steady-state thermal population. Next, using two KOs, we demonstrate logical control and dynamical protection of a dual-rail qubit with nearly fourfold erasure bias. Finally, using a single end-of-circuit erasure check, we achieve an error per Clifford of 5.6×10−4, which falls to 1.5×10−4 after post-selection, with 25~ns gates.