The circuit dynamics of power networks are typically neglected in transient stability analysis of power systems. While this approximation is justified in classical multi-machine power systems, the circuit dynamics can compromise stability of power systems dominated by grid-forming (GFM) power converters. In this work, we show that the impact of circuit dynamics can be mitigated by (i) augmenting GFM droop control with derivative feedback, and (ii) leveraging derivative control terms of dual-port GFM control that was recently proposed in the literature. Moreover, we show that, contrary to conventional wisdom, avoiding instability by slowing down the converter dynamics (e.g., through virtual inertia) is not always possible or may require unrealistic virtual inertia constants.