The strict momentum conservation constraints for backward-wave optical parametric oscillators (BWOPOs) gives an inherently narrowband backward-generated wave, even with broadband pumping. Unfortunately, the limited tuning range of this wave restricts potential applications. Here we demonstrate a method to circumvent this restriction and increase the tuning range by more than one order of magnitude. A linearly chirped pump modulation is transferred to the forward-generated BWOPO wave, which is then mixed with an identically chirped pump in a conventional optical parametric amplifier to obtain narrowband (38 GHz), broadly tunable, infrared radiation around 1.86 µm, with an output energy of 19 µJ.