Resonant dispersive wave (RDW) emission in gas-filled hollow waveguides is a powerful technique for the generation of bright few-femtosecond laser pulses from the vacuum ultraviolet to the near infrared. Here, we investigate deep-ultraviolet RDW emission in a hollow capillary fiber filled with a longitudinal gas pressure gradient. We obtain broadly similar emission to the constant-pressure case by applying a surprisingly simple scaling rule for the gas pressure and study the energy-dependent dispersive wave spectrum in detail using simulations. We further find that in addition to enabling dispersion-free delivery to experimental targets, a decreasing gradient also reduces the pulse stretching within the waveguide itself, and that transform-limited pulses with 3 fs duration can be generated by using short waveguides. Our results illuminate the fundamental dynamics underlying this frequency conversion technique and will aid in fully exploiting it for applications in ultrafast science and beyond.