This paper addresses stability challenges in Dual Active Bridge (DAB) converters with input LC filter, increasingly adopted in emerging DC grids. The targeted system is studied in response to wide supply voltage variations in both steady-state and transient conditions. Although numerous Modulation Schemes (MSs) are developed to optimize efficiency, their impact on stability has not been fully addressed in literature. In response, a novel method for informed MS design based on small-signal stability analysis is proposed. To that end, the closed-loop input impedance of the converter is modeled with full consideration of the MS and controller parameters. The impact of an Active Damping (AD) strategy is even considered for stability margin enhancement, thus allowing for the design and experimental validation of an informed MS that strikes a balance between stability and efficiency.